Time-frequency Analysis Research Articles

A novel hybrid method for predicting maglev train-induced environmental vibrations combining field measurement, 2.5D FEM modelling and multi-objective optimization

The maglev system has been developed rapidly in recently years since its advantage in mass transportation, ride comfort and energy efficiency, which also caused an increasing concern on the maglev train-induced environmental vibrations. This paper presents a novel hybrid framework for predicting high-speed maglev train-induced environmental vibrations combining field measurement, 2.5D FEM simulation and multi-objective optimization. First, a maglev train-guideway-soil coupled model considering guideway irregularities was proposed to calculate the ground vibration using 2.5D FEM. Then, the guideway irregularity spectrum and soil damping are inverted by the optimization process using the NSGA3 genetic algorithm, in which the differences of measured and calculated vertical vibrations of measuring points are chosen as objective functions. With the inverted guideway irregularity spectrum and soil damping, the ground vibrations were calculated using the 2.5D FEM model and compared with the field measurements. It was found that the inverted PSD spectrum of guideway irregularity generally decreases as the spatial frequency increases, exhibiting a similar trend as the measured ones. The results obtained by the proposed hybrid prediction method agree well with the field measurement in both time domain and frequency domain. The prediction error for the vertical vibration level of all measuring points induced by five maglev train passing are mainly less than 10 %, indicating that the proposed hybrid method provided a reliable and effective method for vibration prediction combining field measurement and numerical simulation.

Digital twin for EEG seizure prediction using time reassigned multisynchrosqueezing transform-based CNN-BiLSTM-attention mechanism model

Abstract The prediction of epileptic seizures is a classical research problem, representing one of the most challenging tasks in the analysis of brain disorders. There is active research into digital twins (DT) for various healthcare applications, as they can transform research into customized and personalized healthcare. The widespread adoption of DT technology relies on ample patient data to ensure precise monitoring and decision-making, leveraging Machine Learning (ML) and Deep Learning (DL) algorithms. Given the non-stationarity of EEG recordings, characterized by substantial frequency variations over time, there is a notable preference for advanced time-frequency methods in seizure prediction. This research proposes a DT-based seizure prediction system by applying an advanced time-frequency analysis approach known as Time-Reassigned MultiSynchroSqueezing Transform (TMSST) to EEG data to extract patient-specific impulse features and subsequently, a Deep Learning strategy, CNN-BiLSTM-Attention mechanism model is utilized in learning and classifying features for seizure prediction. The proposed architecture is named as “Digital Twin-Net”. By estimating the group delay in the time direction, TMSST produces the frequency components that are responsible for the EEG signal’s temporal behavior and those time-frequency signatures are learned by the developed CNN-BiLSTM-Attention mechanism model. Thus the combination acts as a digital twin of a patient for the prediction of epileptic seizures. The experimental results showed that the suggested approach achieved an accuracy of 99.70% when tested on 23 patients from the publicly accessible CHB-MIT dataset. The proposed method surpasses previous solutions in terms of overall performance. Consequently, the suggested method can be regarded as an efficient approach to EEG seizure prediction.

Does aberrant electrocortical dynamics pattern imply atypical balance control in adolescents with idiopathic scoliosis?

Adolescent idiopathic scoliosis (AIS) is a developmental disorder described as a three-dimensional spine deformity with multifactorial etiology. The multifactorial model of AIS suggests that the patient population is diverse. Identifying individuals with sensorimotor control impairments could enable personalized treatments, potentially leading to improved outcomes for those with AIS. We hypothesize that abnormal electrocortical dynamics within the sensorimotor cortex will be related to less efficient balance control in standing during ankle proprioception alteration in the absence or presence of vision. To test this hypothesis, the balance control performance of adolescents with AIS will be assessed on a force platform by computing the root mean square value of the scalar distance between the center of pressure and the center of gravity. Electroencephalography will be recorded while challenging balance control by altering ankle proprioception in the presence and absence of visual cues. Time-frequency analyses will be calculated to determine alpha, and beta band power in both conditions. Pilot data from 13 participants with AIS were analyzed to support our hypothesis. Three participants with less efficient balance control showed electrocortical dynamics changes, such as an increase in beta band power in the presence and absence of vision and a decrease in alpha band power in the presence of vision compared to the AIS group with efficient balance control. These findings support our hypothesis of suboptimal sensorimotor information processing in the subgroup of adolescents with AIS with less efficient balance control, which could have significant implications for developing personalized treatments for AIS.

Surface feature extraction method for cloud data of aircraft wall panel measurement points

In the cloud, users need to connect to the data server to perform the file transmission via the Internet, and the Server transmits data to many servers. A machine or vehicle that can fly with the assistance of the air is known as an Aircraft. As an alternative to the downward thrust of jet engines, it uses either static lift or an airfoil's dynamic lift to combat gravity's pull. Drawing wall panel measurement points in the model is easy using the Aircraft Wall Panels (AWP) button. Draw wall panels between existing nodes or on the drawing grid using the relevant wall panel specifications. The technique intends to discover and extract information about undesirable defects such as dents, protrusions, or scratches based on local surface attributes gathered from a 3D scanner. Defects from a perfectly smooth surface include indentations and bumps on the surface. An image's features may be extracted by reducing the number of pixels in the picture to a manageable size so that the most exciting sections of the image can be recorded with Surface Feature Extraction (SFE). Some of the problems are the threat of drones and composite materials that do not break easily in oxymoronic. The aircraft's inner structure may have been damaged, although this is impossible to determine. A runway incursion severely threatens aviation safety because of the rise in aircraft movement on the airport surface and other human factors. An electronic moving map of airport runways and taxiways is shown to the pilot through a head-up display in the cockpit's head-down position. A practical feature extraction approach is required to ensure the safety of the airport scene in runway incursion prevention systems. All the drawbacks are rectified by AWP-SFE sensors installed along the runway centerline to detect magnetic signals generated by surface-moving targets, and this information is utilized to compute the target's length. The target length may extract peak features after regularizing the time domain data. Differentiation of target characteristics is used to determine the similarities between distinct targets. The suggested method's signal characteristics are more easily recognized than time domain or frequency domain feature methods. The experimental results show the proposed method AWP-SE to achieve a high-efficiency ratio of 88.2%, activity ratio of 73.3%, Analysis of aircraft in wall plane measurement point of 87.8% and an error rate of 32.3% compared to other methods.

Identification of copper and lead pollution elements based on spectra of corn leaves in different leaf layers

With the development of industrialization, environmental heavy metal pollution has become increasingly serious, and the growth of crops has been seriously affected by heavy metal pollution in the soil environment. Therefore, it is necessary to establish methods for distinguishing and monitoring heavy metal pollution. The application of hyperspectral remote sensing in heavy metal pollution monitoring demonstrates the great potential of using crop leaf spectra to accurately distinguish heavy metal pollution elements. At the same time, new spectral processing methods and models are required to provide support for accurate identification. In this study, greenhouse experiments were conducted to simulate the growth of corn plants under heavy metal Cu and Pb stress. Collect hyperspectral data from different leaf layers of maize plants during the heading stage. Multivariate empirical mode decomposition (MEMD) was introduced, and the spectral data were preprocessed using MEMD, First derivative (FD), and second derivative (SD). At the same time, chemical analysis was used to examine the changes in copper (Cu), lead (Pb), and chlorophyll content in corn leaves. Competitive adaptive reweighted sampling (CARS) and iteratively retaining informative variables (IRIV) were used to screen characteristic bands that were sensitive to copper and lead. Finally, machine learning SVM, ELM, and XGBoost were utilized to construct and propose a series of models such as MEMD-CARS-ELM for accurate discrimination of Cu and Pb pollution elements. The results indicated that the discriminative model established after the MEMD transformation of the spectrum exhibited the best performance. Among them, whether it is tender leaves, functional leaves, or basal leaves, the accuracy of the MEMD-CARS-SVM and MEMD-CARS-ELM models in the training group and validation group for distinguishing Cu and Pb elements is greater than 80%. Other models established by MEMD spectral transformation are also significantly better at identifying Cu and Pb than those established by FD and SD transformations. The signal time–frequency analysis method MEMD is feasible and excellent for hyperspectral data processing. Based on this method, the Cu and Pb pollution element identification method proposed in this study was reliable. The research results provide a new method for the preprocessing of hyperspectral data and a new perspective for the accurate identification of soil heavy metal contamination elements. This study showed that corn leaf spectra can be used to accurately identify heavy metal pollution elements, providing a powerful scientific reference for hyperspectral remote sensing to monitor heavy metal pollution in large areas.

The effects of Baduanjin exercise on the psychological condition and heart rate variability of sports-disadvantaged college students: A randomised trial

ObjectiveTo investigate the effects of a 16-week Baduanjin exercise programme on the psychological status and heart rate variability (HRV) of college students in a sports-disadvantaged group, offering a theoretical basis for the potential of Baduanjin exercise to improve mental health.Trial DesignThis prospective study enrolled 93 college students from Wuyi University, exempt from the National Standards for Students’ Physical Health due to illness or disability. The participants were divided into a control group (n = 47) and an experimental group (n = 46). Over 16 weeks, the experimental group engaged in the Baduanjin exercise, whereas the control group did not participate in regular physical training.MethodsWe assessed the Symptom Checklist-90-Revised (SCL-90-R, the primary outcome) scores and HRV (time domain and frequency domain indices, the secondary outcomes) of all participants both before and after the 16-week programme.Results(1) Post-16 weeks of Baduanjin exercise, a statistically significant difference was observed in the SCL-90-R scores between the control and experimental groups (P < 0.01, P < 0.05). Notably, the scores for interpersonal sensitivity, depression, anxiety, psychoticism, and other factors (predominantly relating to sleep and diet) were significantly lower in the experimental group (t = 4.234, 2.616, 3.450, 2.226, 3.980, P < 0.01, P < 0.05). (2) Following the exercise regimen, the experimental group showed a substantial decrease in heart rate, low-frequency (LF) power, and the LF/high-frequency ratio (LF/HF ratio), and a significant increase in HF compared with the control group (t = 2.358, 4.528, − 2.595, P < 0.05 P < 0.01).ConclusionSixteen weeks of Baduanjin exercise may substantially enhance HRV, potentially aiding in balancing sympathetic–vagal nerve activity and thus contributing to the regulation of mental health.

Probability analysis of compressor blade vibration based on radial basis function extremum neural network method

To enhance the transient response and modeling accuracy of compressor blade vibration characteristics in time domain dynamic reliability analysis, a method called the radial basis function extremum neural network (RBFENN) is proposed. This method combines the radial basis function neural network (RBFNN) with the extreme response surface method (ERSM). By considering the time domain and frequency domain characteristics of unsteady aerodynamic excitation on blades affected by multi-row stator/rotor interference, the stress response distribution of the blades is determined through deterministic analysis. The RBFENN mathematical model is established using RBFNN to address the high nonlinearity in surrogate modeling. The ERSM is used to process the transient problem of motion reliability analysis, taking extreme values into account throughout the response process. In evaluating the vibrational reliability of the compressor blades, the maximum stress is considered as the primary focus of the study, taking into account the stochastic nature of aerodynamic excitation frequency, rotational velocity, and material parameters. It is observed that the unsteady aerodynamic excitation induces higher-order harmonic resonances in the blade velocity margin, resulting in increased stress at the leading edge of the blade root. This stress distribution follows a normal distribution pattern. A comparison among Monte Carlo methods, ERSM, and RBFENN demonstrates the superiority of the proposed RBFENN method in terms of computational accuracy and efficiency. This study introduces the RBFENN method as a learning-based approach for blade vibration reliability design, enriching the theory of mechanical reliability.

Acoustic emission evolution and fracture mechanism of rock for direct tensile failure

The failure mechanisms of engineering rock masses primarily involve tensile and shear failure. Differentiating between the acoustic emission (AE) signals generated during the tensile and shear damage processes in rock can provide a scientific basis for the classification of acoustic signals in field rock fracture monitoring. This paper presents a study on acoustic emission monitoring during the direct tensile testing of granite, proposing a method for classifying AE signals based on the damage and failure processes of the samples. Additionally, the classification of tensile and shear AE signals is explored. The main conclusions are as follows. The proportion of low-frequency signals (frequency <200 kHz) and high-frequency signals (frequency >200 kHz) in all AE signals was found to be 81.6 % and 19.4 %, respectively. Based on an integrated classification and statistical method for AE signals in rock tensile failure, which involves steps such as “denoising the raw waveform, time-frequency domain data transformation, fuzzification processing, extraction of dominant frequency and corresponding amplitude, and identification of secondary dominant frequencies,” the AE signals were categorized into two types, A and B. Type A signals accounted for an average of 7.6 %, while Type B signals made up 92.4 %. Based on the polarity determination method, the focal mechanisms of AE (Acoustic Emission) events were identified. In tensile events, the average proportion of Type A signals was 8.34 %, while the average proportion of Type B signals was 91.66 %. The Brazilian splitting test also yielded classification results similar to those obtained from direct tensile testing. Thus, it was preliminarily concluded that Type A signals, characterized by the presence of both a primary and secondary frequency, correspond to shear signals, whereas Type B signals, which only exhibit a primary frequency without a secondary frequency, correspond to tensile signals.

ABAQUS-based research on the parameters of highway subgrade vibratory compaction and vibration wave propagation laws

Vibratory rollers are generally used in the process of highway subgrade compaction. In the paper, the vibratory roller—subgrade finite element model was established to simulate the field construction by using ABAQUS. We used Hilbert–Huang Transform to analyze the compaction in the field test from the time–frequency domain. By changing the parameters of the vibratory roller and the filler, the comprehensive influence of the parameters such as the elastic modulus of the filler, rolling speed, excitation force, vibration frequency and thickness of the filler on the compaction quality of the subgrade was investigated. We studied the propagation pattern of vibration waves in three-dimensional space. The study shows that the signals of different frequency bands in the Hilbert spectrum represent the compaction degrees of fillers in different zones. The peak acceleration generally decreases with the increase of horizontal and vertical distance, but there is an increase at the boundary of the vibration field. There is an optimal combination of the excitation force, vibration frequency and thickness of the filler. The vibration waves propagate in the form of an ellipsoid in three dimensions, and the amplitude decreases with distance.

Distinguishing among standing postures with machine learning-based classification algorithms.

The purpose of our study was to evaluate the accuracy with which classification algorithms could distinguish among standing postures based on center-of-pressure (CoP) trajectories. We performed a secondary analysis of published data from three studies: Study A) assessment of balance control on firm or foam surfaces with eyes-open or closed, Study B) quantification of postural sway in forward-backward and side-to-side directions during four standing-balance tasks that differed in difficulty, and Study C) an evaluation of the impact of two modes of transcutaneous electrical nerve stimulation on balance control in older adults. Three classification algorithms (decision tree, random forest, and k-nearest neighbor) were used to classify standing postures based on the extracted features from CoP trajectories in both the time and time-frequency domains. Such classifications enable the identification of differences and similarities in control strategy. Our results, especially those involving time-frequency features, demonstrated that distinct CoP trajectories could be identified from the extracted features in all conditions and postures in each study. Although the overall classification accuracy was similar using time-frequency features (~ 86%) for the three studies, there were substantial differences in accuracy across conditions and postures in Studies A and B but not in Study C. Nonetheless, the models were far superior to the published results with conventional metrics in distinguishing between the conditions and postures. Moreover, a Shapley Additive exPlanation analysis was able to identify the most important features that contributed to the classification performance of the models.

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GDTE-based crack diagnosis for planetary gear: Mechanism, validation, and advantages compared to vibration-based technology

Effective health monitoring and fault diagnosis technologies are crucial to timely grasping the operation status of the planetary gear train (PGT). In this study, the mechanism for global dynamic transmission error (GDTE)-based crack diagnosis of PGT is revealed from dynamic responses and validated through experiments, and the advantages of this new technique are compared with the commonly used vibration-based technology. Initially, a dynamic model of the PGT considering various crack degrees and transfer path effects is established, and the effectiveness of the model response is verified through experiment. Subsequently, GDTE and vibration signals under different crack conditions are statistically analyzed in time domain and frequency domain to evaluate the differences in the ability to reveal gear failure information. Ultimately, the reasons for the different distribution of fault characterization information in the two signals are explained from a dynamic perspective. The results show that GDTE-based fault diagnosis exhibits greater sensitivity to gear crack degree compared to vibration-based monitoring technology, with both time and frequency domain responses containing richer fault characteristic information, particularly in low-frequency regions. The fault characteristics concentrated in higher-frequency regions in the vibration signal are mainly caused by the modulation between gear crack shock and the gear single and double tooth alternating meshing shock. Conversely, fault frequencies in GDTE signals are mainly found in low-frequency regions, as fault shocks in GDTE signals directly correlate with the rotational frequency of the cracked gear. Modulation effects and attenuation on the transfer path are identified as the main reasons for the weaker representation of gear fault information in vibration signals compared to GDTE signals.

Approximation of Time-Frequency Shift Equivariant Maps by Neural Networks

Based on finite-dimensional time-frequency analysis, we study the properties of time-frequency shift equivariant maps that are generally nonlinear. We first establish a one-to-one correspondence between Λ-equivariant maps and certain phase-homogeneous functions and also provide a reconstruction formula that expresses Λ-equivariant maps in terms of these phase-homogeneous functions, leading to a deeper understanding of the class of Λ-equivariant maps. Next, we consider the approximation of Λ-equivariant maps by neural networks. In the case where Λ is a cyclic subgroup of order N in ZN×ZN, we prove that every Λ-equivariant map can be approximated by a shallow neural network whose affine linear maps are simply linear combinations of time-frequency shifts by Λ. This aligns well with the proven suitability of convolutional neural networks (CNNs) in tasks requiring translation equivariance, particularly in image and signal processing applications.

Effects of 1267 nm Illumination on Microcirculation Regulatory Mechanisms.

This study explored the effects of 1267 nm laser irradiation on changes in blood flow parameters and activation of the regulatory mechanisms of the microcirculatory bed (MCB). Using laser Doppler flowmetry (LDF) technique and time-frequency analysis of perfusion signals, changes in the MCB of 16 healthy volunteers, targeting the distal phalanx of the third finger with 1267 nm laser irradiation were evaluated. Results indicated no significant differences in perfusion between control and target measurements, likely due to blood flow redistribution caused by vessel dilation/constriction. However, differences in oscillation amplitudes in endothelial and myogenic ranges were observed, suggesting microcirculation self-regulation. Detailed analysis revealed characteristic peaks in the endothelial range during and after irradiation, indicating endothelial mediator release. It is assumed that the identified effects may be related to the singlet oxygen generated by 1267 nm laser irradiation, which directly affects the MCB, manifesting as endothelium-dependent vascular activity.

Electroencephalogram-based time-frequency analysis for Alzheimer’s disease detection using machine learning

Background: Alzheimer&amp;rsquo;s disease (AD) is the most common form of dementia. The lack of effective prevention or cure makes AD a significant concern, as it is a progressive disease with symptoms that worsen over time. Objective: The aim of this study is to develop an algorithm capable of differentiating between patients with early-stage AD (mild cognitive impairment [MCI]), moderate AD, and healthy controls (C) using electroencephalogram (EEG) signals. Methods: A publicly available EEG database was utilized, with seven EEG recordings selected from each study group (MCI, AD, and C) to ensure a balanced dataset. For each 1-s segment of EEG data, 43 time-frequency features were computed. These features were then compressed over time using 10 statistical measures. Subsequently, 15 classifiers were employed to distinguish between paired groups using a 7-fold cross-validation. Results: The strategy yielded better results than state-of-the-art methods, achieving a 100% accuracy in both C versus MCI and C versus AD binary classifications. This improvement translated to a 2% increase in accuracy for C versus MCI and a 4% increase for C versus AD, despite a 1.2% decrease in performance for AD versus MCI. In addition, the proposed method outperformed prior work on the same database by 4.8% for the AD versus MCI comparison. Conclusion: The present study highlights the potential of EEG as a promising tool for early AD diagnosis. Nevertheless, a more extensive database should be used to enhance the generalizability of the results in future work.

Generalized reassigning transform: Algorithm and applications

Time-frequency analysis (TFA) has attracted the attention of many scholars and engineers for analyzing nonstationary signals in the field of condition monitoring of rotating machinery. For complex mechanical equipment, measured signals always contain both harmonic and impulsive components, which presents a challenge for current TFA methods. To concurrently characterize harmonic and impulsive components, a novel TFA algorithm, called generalized reassigning transform (GRT) is developed in this paper. First, the time-frequency fusion extraction criterion (TFFEC), which includes time-frequency data fusion (TFDF) and time-frequency data extraction (TFDE), is designed to calculate time-frequency representation (TFR) from short-time Fourier transform (STFT) results under different window sizes, which improves time-frequency resolution and eliminates noise influence. Furthermore, the chirp rate (CR)-based postprocessing strategy is constructed to characterize nonstationary signals with both harmonic-like and impulsive-like components. Specifically, the CR discrimination criterion is introduced to classify the TFFEC result into two distinct types: harmonic-like component and impulsive-like component, and then, the TFR with high energy concentration and strong readability is obtained by advanced postprocessing TFA including the synchro-reassigning transform (SRT) and horizontal reassigning transform (HRT). The effectiveness of the GRT in condition monitoring and fault diagnosis is validated through numerical and experiment verification.

Investigation of three-dimensional forces during additive friction stir deposition — How could force signals reveal the deposition quality?

Additive friction stir deposition (AFSD) is a solid-phase forming technology based on microzone forging, which is essentially a force-driven additive manufacturing process. This work focuses on the effects of the AFSD parameters on the force signals and forming quality, which is highly important for optimizing the process parameters and controlling the forming quality. By analyzing the force features in the time‒frequency domain, the evolution mechanism of three-dimensional forces during AFSD was explored. A 3D scanner, scanning electron microscope (SEM) and electron backscatter diffraction (EBSD) were used to clarify the surface morphology and microstructures of the deposition layers. It was found that deposition defects were accompanied by a lack of plasticization or nonuniform deformation between the advancing side (AS) and the retreating side (RS). Moreover, the relationships among the process parameters, three-dimensional forces and deposition quality were investigated. It is proved that force signal can effectively reflect the deposition quality. A comprehensive prediction model based on three-dimensional force features was developed, achieving an accurate prediction of deposition quality. Furthermore, this work demonstrated the feasibility of AFSD quality control on the basis of force signals. The currently employed control strategies can be further extended to address the AFSD of large components in the future.

Non-linear dynamic behavior of T0 and T90 mesopelagic trawls based on the Hilbert–Huang transform

Although adopting the T90 mesh orientation on the trawl net can improve the selectivity of the trawl codend, it is unknown whether the T90 mesh orientation influences the dynamic behavior of the trawl system. Therefore, this study uses non-linear dynamic analysis to examine the effect of mesh orientations, mesh size, and twine diameter on the mesopelagic trawls' fluttering motions and hydrodynamic force responses. Three trawls are designed with different mesh orientations (T0 and T90), mesh sizes (40 mm and 60 mm), and twine diameters (0.96 mm and 1.11 mm) on the codend and codend extension sections of the trawl model based on Tauti's law. These trawls are tested in a flume tank under various flow velocities and catch sizes. A time-frequency analysis method based on the Hilbert–Huang transform is utilized to analyze each trawl's dynamic responses, including motions and drag force responses. The results are compared with those obtained through Fourier analysis using power spectral density. The results highlight that the oscillation amplitude of the surge motion of the T90 trawl is higher than that of the T0 trawl. In contrast, the T90 trawl's heave motion oscillation amplitude is smaller. The dominant frequency of the periodic high-energy coherent structures of the surge and heave motions are detected at a low frequency. The surge and heave motions of the T0 trawl have a greater response to the current components with lower frequencies than that of the T90 trawl. An increase in mesh size, a decrease in twine diameter, and a change in mesh orientation decrease the drag force. The inherent characteristic oscillations of the drag force response for the three trawl models are synchronized with the low-frequency characteristic of surge and heave motions. The gravity periods of the low-frequency mode components of drag force, surge motion, and heave motion for the T90 trawl are higher than those for the T0 trawls. In other words, the T90 trawl is more stable and selective than the T0 trawl. The findings of this study offer important information for comprehending and enhancing the selectivity of trawls in marine mesopelagic fisheries, particularly for exposing the effects of mesh orientation and design parameters on trawl performances.

Time-frequency reassignment of blade tip timing signal

The health condition of a rotor blade can be assessed by its dynamic frequency with respect the rotational speed, which can be derived from the time–frequency analysis of the blade vibration signal. Blade tip timing (BTT), as a non-contact measurement technique, provides an alternative to traditional contact strain measurement methods. However, the vibration signal measured by BTT is usually undersampled, which limits the application of conventional time–frequency analysis methods. BTT sparse time–frequency methods utilize the sparsity to reconstruct undersampled BTT signals. Nevertheless, BTT sparse time–frequency representation suffers from poor concentration and inaccurate estimation of the dynamic frequency, especially in the case of fast varying speed and limited BTT sensors. In this paper, a BTT time–frequency reassignment method is proposed to enhance the concentration of the BTT time–frequency spectrum and improve the accuracy of dynamic frequency estimation. Firstly, BTT time–frequency reassignment utilizes the blade natural frequency, obtained from the Campbell diagram, as prior information. The blade dynamic frequency with respect to the rotational speed is estimated by combining the prior frequency with the measured frequency in the Bayesian framework. Subsequently, weights are assigned to both the time–frequency coefficients and the posterior frequency. The time–frequency coefficients are relocated around the posterior frequency according to the weights. The advantages of BTT time–frequency reassignment are demonstrated through a simulation, a laboratory test and a full-scale aeroengine test. Both simulation and experimental results demonstrate that BTT time–frequency reassignment enhances the concentration of the BTT time–frequency spectrum and improves the accuracy of the estimated dynamic frequency when limited BTT sensors are available. The influence of the prior frequency is discussed to evaluate the robustness of BTT time–frequency reassignment. In the full-scale aeroengine test, the reliability of BTT time–frequency reassignment is verified under the fast varying speed.

Cutting force reconstruction method based on static bandwidth expansion utilizing acceleration sensors

The cutting force is the most direct indicator reflecting tool wear and machining quality. However, direct cutting force measurement equipment requires high costs and will alter dynamic performance, making it difficult to apply in actual production. A single accelerometer can reconstruct the high-frequency dynamic alternating current (AC) components, but it is limited by bandwidth and cannot accurately reconstruct the low-frequency static direct current (DC) components. To address the existing problems of inaccurate reconstruction for the DC components, this article proposes a static bandwidth expansion technology (BET) using acceleration sensors with regard to its application in the field of broaching. BET reconstructs the low-frequency DC components of the broaching force using the AC components obtained from acceleration signals and the metal cutting area. The AC components of the broaching force are reconstructed from acceleration signals through double integration, combined with a Kalman filter that incorporates dynamic parameters. The complete broaching force signal can be obtained by fusing the AC and DC components. BET overcomes the problem of low-frequency bandwidth distortion in the accelerometer sensor and successfully expands the low-frequency bandwidth of the accelerometer sensor, achieving the function of reconstructing cutting force with a single accelerometer sensor. This technology is applied in the actual machining process, and the reconstructed broaching force based on BET has a high degree of coincidence with the experimentally obtained broaching force in the time-frequency domain.