Time-frequency Methods Research Articles

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.

Decoding sensorimotor information from somatosensory cortex by flexible epicortical μECoG arrays in unrestrained behaving rats

Objective.Brain-computer interfaces (BCI) are promising for severe neurological conditions and there are ongoing efforts to develop state-of-the-art neural interfaces, hardware, and software tools. We tested the potential of novel reduced graphene oxide (rGO) electrodes implanted epidurally over the hind limb representation of the primary somatosensory (S1) cortex of rats, and compared them to commercial platinum-iridium (Pt-Ir) 16-channel electrodes (active site diameter: 25μm).Approach.Motor and somatosensory information was decoded offline from microelectrocorticography (μECoG) signals recorded while unrestrained rats performed a simple behavioral task: pressing a lever and the subsequent vibrotactile stimulation of the glabrous skin at three displacement amplitude levels and at two sinusoidal frequencies.μECoG data were initially analyzed by standard time-frequency methods. Next, signal powers of oscillatory bands recorded from multiple electrode channels were used as features for sensorimotor classification by a machine learning algorithm.Main results.Both electrode types performed quite well and similar to each other for predicting the motor interval and the presence of the vibrotactile stimulus. Average accuracies were relatively lower for predicting 3-class vibrotactile frequency and 4-class amplitude level by both electrode types.Significance.Given some confounding factors during the free movement of rats, the results show that both sensory and motor information can be recorded reliably from the hind limb area of S1 cortex by usingμECoG arrays. The chronic use of novel rGO electrodes was demonstrated successfully. The hind limb area may be convenient for the future evaluation of new tools in neurotechnology, especially those for bidirectional BCIs.

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.

Long-Term Impacts of Runoff and Coastal Reclamation on Tidal Bore Variations in the Qiantang River Estuary, China

Tidal bore dynamics in estuarine environments are influenced by both natural hydrological changes and human activities, such as coastal reclamation. This study focuses on the Qiantang River estuary, assessing the impacts of runoff variations and reclamation on tidal bores over the past five decades. By employing statistical and time-frequency methods, including the Mann–Kendall test, ordered clustering, and wavelet analysis, the relationships between tidal bore height, river discharge, and reclamation activities are examined. The results indicate that increased freshwater discharge reduces bore intensity over short timescales of 0.3 to 1.2 years, while decreased runoff amplifies it. Over longer periods of 4.1 to 8.3 years, a positive correlation emerges, with changes in runoff preceding variations in tidal bore height. Coastal reclamation, particularly the narrowing of channels, has significantly reduced the bore height at Yanguan, especially in the years following the 2000s. Additionally, the long-term interactions of other factors influencing tidal bores are explored. These findings reveal a delayed estuarine response to human modifications, highlighting the necessity of long-term monitoring and adaptive management strategies to mitigate these impacts. The study provides valuable insights into the complex interplay of natural and human factors, offering guidance for future estuarine management and conservation efforts.

Time-varying cable force identification in cable-stayed bridges by a high-resolution time-frequency method

Accurate monitoring of time-varying cable force plays a vital role in the condition assessment of cables. However, most current methods for identifying the cable force can only provide an average cable force over a period. The vibration method correlates the cable force with cable frequency via a formula, transforming the time-varying cable force identification into the instantaneous frequency (IF) identification of the cable. Synchroextracting transform (SET) is a powerful time-frequency method with the ability to identify the cable’s IF from the measured response. However, the performance of SET in identifying the IF is heavily influenced by the choice of window length, limiting its practical application. In this study, an improved SET (ISET) is proposed to overcome this limitation and is utilized to identify the time-varying force in bridge cables. In ISET, the variational mode decomposition is first employed to decompose the measured response into several mono-component modes. A hyperparameter optimization algorithm, adopting Rényi entropy as the evaluation index, is then introduced to determine the optimal window length for each mono-component mode. Furthermore, the proposed ISET with the optimal window length is used to identify the cable’s IF, thereby calculating the time-varying cable force using the vibration method formula. Cases involving finite element model of the cable, along with laboratory experiments on a scaled cable, show that the proposed method successfully addresses the limitations of SET and accurately identifies time-varying cable force. Finally, to validate the practicality of the proposed method, the field test data from an unsymmetric cable-stayed bridge is adopted. The results demonstrate that the proposed method is straightforward and efficient, capable of accurately monitoring the time-varying cable force in both new and existing cables of cable-stayed bridges.

Time-varying characteristics analysis of bridge under moving vehicle using a modified time-frequency method with limited sensors

Investigating the bridge dynamic characteristics under operational traffic load is critical for bridge health monitoring. As vehicles traverse the bridge, the bridge frequencies present time-varying characteristics owing to the effect of vehicle-bridge dynamic interaction. The recently introduced variational nonlinear chirp mode decomposition (VNCMD) demonstrates significant benefits in identifying structural instantaneous frequencies (IFs) from the measured responses. However, its practical application is limited by the requirement for artificially setting priori parameters (i.e., upper bound of noise level and number of modal components). In this study, a modified VNCMD (MVNCMD) is proposed to overcome this limitation and is employed to identify the IFs of the bridge under moving vehicle using single sensor data. First, by modifying the optimization function, the proposed MVNCMD adopts a novel algorithm framework that eliminates the necessity for presetting the upper bound of noise level. An autoregressive spectrum-based method is then introduced to preset the number of modal components. The proposed MVNCMD is evaluated using a synthetic non-stationary signal, demonstrating its effectiveness in identifying IFs and overcoming the limitations of the original VNCMD. Furthermore, the numerical simulation involving different parameter analysis and laboratory experiments of the coupled vehicle-bridge system are conducted to validate the effectiveness of the proposed method. It is to be shown that the proposed MVNCMD method is capable of identifying the IFs of the bridge under moving vehicle using single sensor data and outperforms other time-frequency methods in terms of identification accuracy, which provides a robust tool for analyzing the time-varying characteristics of the vehicle-bridge interaction system.

Exploring the potential of pretrained CNNs and time-frequency methods for accurate epileptic EEG classification: a comparative study

Prompt diagnosis of epilepsy relies on accurate classification of automated electroencephalogram (EEG) signals. Several approaches have been developed to characterize epileptic EEG data; however, none of them have exploited time-frequency data to evaluate the effect of tweaking parameters in pretrained frameworks for EEG data classification. This study compares the performance of several pretrained convolutional neural networks (CNNs) namely, AlexNet, GoogLeNet, MobileNetV2, ResNet-18 and SqueezeNet for the localization of epilepsy EEG data using various time-frequency data representation algorithms. Continuous wavelet transform (CWT), empirical Fourier decomposition (EFD), empirical mode decomposition (EMD), empirical wavelet transform (EWT), and variational mode decomposition (VMD) were exploited for the acquisition of 2D scalograms from 1D data. The research evaluates the effect of multiple factors, including noisy versus denoised scalograms, different optimizers, learning rates, single versus dual channels, model size, and computational time consumption. The benchmark Bern-Barcelona EEG dataset is used for testing purpose. Results obtained show that the combination of MobileNetV2, Continuous Wavelet Transform (CWT) and Adam optimizer at a learning rate of 10−4, coupled with dual-data channels, provides the best performance metrics. Specifically, these parameters result in optimal sensitivity, specificity, f1-score, and classification accuracy, with respective values of 96.06%, 96.15%, 96.08%, and 96.10%. To further corroborate the efficacy of opted pretrained models on exploited Signal Decomposition (SD) algorithms, the classifiers are also being simulated on Temple University database at pinnacle modeling composition. A similar pattern in the outcome readily validate the findings of our study and robustness of deep learning models on epilepsy EEG scalograms.The conclusions drawn emphasize the potential of pretrained CNN-based models to create a robust, automated system for diagnosing epileptiform. Furthermore, the study offers insights into the effectiveness of varying time-frequency techniques and classifier parameters for classifying epileptic EEG data.

Predicting lever press in a vibrotactile yes/no detection task from S1 cortex of freely behaving rats by µECoG arrays

Aim of the Study Brain-computer interfaces (BCIs) may help patients with severe neurological deficits communicate with the external world. Based on microelectrocorticography (µECoG) data recorded from the primary somatosensory cortex (S1) of unrestrained behaving rats, this study attempts to decode lever presses in a psychophysical detection task by using machine learning algorithms. Materials and Methods 16-channel Pt-Ir microelectrode arrays were implanted on the S1 of two rats, and µECoG was recorded during a vibrotactile yes/no detection task. For this task, the rats were trained to press the right lever when they detected the vibrotactile stimulus and the left lever when they did not. The multichannel µECoG data was analysed offline by time-frequency methods and its features were used for binary classification of the lever press at each trial. Several machine learning algorithms were tested as such. Results The psychophysical sensitivities (A') were similar and low for both rats (0.58). Rat 2 (B'': −0.11) had higher bias for the right lever than Rat 1 (B'': − 0.01). The lever presses could be predicted with accuracies over 66% with all the tested algorithms, and the highest average accuracy (78%) was with the support vector machine. Conclusion According to the recent studies, sensory feedback increases the benefit of the BCIs. The current proof-of-concept study shows that lever presses can be decoded from the S1; therefore, this area may be utilised for a bidirectional BCI in the future.

Convolutional Neural Networks for Local Component Number Estimation from Time–Frequency Distributions of Multicomponent Nonstationary Signals

Frequency-modulated (FM) signals, prevalent across various applied disciplines, exhibit time-dependent frequencies and a multicomponent nature necessitating the utilization of time-frequency methods. Accurately determining the number of components in such signals is crucial for various applications reliant on this metric. However, this poses a challenge, particularly amidst interfering components of varying amplitudes in noisy environments. While the localized Rényi entropy (LRE) method is effective for component counting, its accuracy significantly diminishes when analyzing signals with intersecting components, components that deviate from the time axis, and components with different amplitudes. This paper addresses these limitations and proposes a convolutional neural network-based (CNN) approach for determining the local number of components using a time–frequency distribution of a signal as input. A comprehensive training set comprising single and multicomponent linear and quadratic FM components with diverse time and frequency supports has been constructed, emphasizing special cases of noisy signals with intersecting components and differing amplitudes. The results demonstrate that the estimated component numbers outperform those obtained using the LRE method for considered noisy multicomponent synthetic signals. Furthermore, we validate the efficacy of the proposed CNN approach on real-world gravitational and electroencephalogram signals, underscoring its robustness and applicability across different signal types and conditions.

FPGA-Microprocessor Based Sensor for Faults Detection in Induction Motors Using Time-Frequency and Machine Learning Methods.

Induction motors (IM) play a fundamental role in the industrial sector because they are robust, efficient, and low-cost machines. Changes in the environment, installation errors, or modifications to working conditions can generate faults in induction motors. The trend on IM fault detection is focused on the design techniques and sensors capable of evaluating multiple faults with various signals using non-invasive analysis. The methodology is based on processing electric current signals by applying the short-time Fourier transform (STFT). Additionally, the computation of the mean and standard deviation of infrared thermograms is proposed as main indicators. The proposed system combines both parameters by means of Support Vector Machine and k-nearest-neighbor classifiers. The development of the diagnostic system was done with digital hardware implementations using a Xilinx PYNQ Z2 card that integrates an FPGA with a microprocessor, thus taking advantage of the acquisition and processing of digital signals and images in hardware. The proposed method has proved to be effective for the classification of healthy (HLT), misalignment (MAMT), unbalance (UNB), damaged bearing (BDF), and broken rotor bar (BRB) faults with an accuracy close to 99%.

Mobile measurement background quantification methods for determining local traffic emissions and background source contributions to ammonia

On-road ammonia (NH3) could be critical for public health in high-population areas due to its contribution to fine particulate matter (PM2.5) formation. Therefore, quantifying the impact of vehicular NH3 emissions on pollution levels is vital from both policy and exposure perspectives. In this study, we conducted night- and daytime mobile measurements during a pollution episode in March 2021, explored common data processing strategies for background concentration estimation and calculated the vehicle contribution in urban Beijing. Percentile and time–frequency methods were evaluated and applied to separate local vehicle and background concentrations. The spatial distributions differed between the night- and daytime periods. However, vehicular emissions were an important source of NH3 both at night and during the day. In the pollution accumulation process, the vehicle contribution increased to 27.4%. Even though local traffic emissions notably impacted NH3 levels, the background concentration, including regional transport, was the largest contributor to NH3 at the city scale. This study has implications for local and regional NH3 control strategies aimed at reducing pollution in densely populated urban areas.

Very short time Fourier transform for turbulent analysis

Nominally stationary acoustic sensors, e.g., buoy suspended or bottom anchored, are subject to various environmental flows. Direct numerical simulation of hydrodynamic flow around the acoustic sensor housing show turbulence along the housing surface. Time-space analysis of pressure variation along the surface of the housing shows significant acoustic-like surface interaction at low frequencies, even at very low mean flow velocity. In this case turbulence manifests as intermittently generated, irregular, coherent vortex structures that separate from the surface of the housing and advect downstream. These structures drive rapid surface pressure transients that propagate within the housing to the acoustic sensors as noise. Fractional Fourier Analysis provides joint time-frequency methods to extract transient features of turbulence. Use of Hermite-Gauss functions and phase relations are of particular interest. [This research is supported by 6.2 NRL base program sponsored by the Office of Naval Research. Distribution Statement A: Approved for public release. Distribution unlimited.]

Single channel blind source separation of rolling bearing compound faults based on self-learning sparse decomposition and feature mode decomposition

Feature mode decomposition (FMD) has advantages over the other newer time-frequency methods such as ensemble empirical mode decomposition (EEMD) and variational mode decomposition (VMD) in single channel blind source separation (SCBSS). However, FMD has the defect of needing to determine the precise number of fault sources manually. To solve the above defect of FMD, an adaptive method for determining the number of fault sources based on the shift invariant sparse code (SISC) is proposed. SISC was used to train a set of basis functions from the single channel signal, and the corresponding potential components were reconstructed firstly. Subsequently, the structural similarity of these potential components was used for clustering, and each of the obtained clustering signals represented one kind of fault. Then the number of clustering was determined by minimizing the structural correlation among the clustering signals. It was considered that the source separation had achieved the best effect when the structural difference among the clusters was the largest, and the number of clustering at this time was used as the optimal estimated value, which was used as the modal inputs number of FMD calculation model to realize SCBSS of rolling bearing. Simulation and experimental analysis were carried out to verify the effectiveness of the proposed method, and its superiority was also verified through comparison.

An Accelerometer-Based Wearable Patch for Robust Respiratory Rate and Wheeze Detection Using Deep Learning.

Wheezing is a critical indicator of various respiratory conditions, including asthma and chronic obstructive pulmonary disease (COPD). Current diagnosis relies on subjective lung auscultation by physicians. Enabling this capability via a low-profile, objective wearable device for remote patient monitoring (RPM) could offer pre-emptive, accurate respiratory data to patients. With this goal as our aim, we used a low-profile accelerometer-based wearable system that utilizes deep learning to objectively detect wheezing along with respiration rate using a single sensor. The miniature patch consists of a sensitive wideband MEMS accelerometer and low-noise CMOS interface electronics on a small board, which was then placed on nine conventional lung auscultation sites on the patient's chest walls to capture the pulmonary-induced vibrations (PIVs). A deep learning model was developed and compared with a deterministic time-frequency method to objectively detect wheezing in the PIV signals using data captured from 52 diverse patients with respiratory diseases. The wearable accelerometer patch, paired with the deep learning model, demonstrated high fidelity in capturing and detecting respiratory wheezes and patterns across diverse and pertinent settings. It achieved accuracy, sensitivity, and specificity of 95%, 96%, and 93%, respectively, with an AUC of 0.99 on the test set-outperforming the deterministic time-frequency approach. Furthermore, the accelerometer patch outperforms the digital stethoscopes in sound analysis while offering immunity to ambient sounds, which not only enhances data quality and performance for computational wheeze detection by a significant margin but also provides a robust sensor solution that can quantify respiration patterns simultaneously.

Application of second order multi-synchrosqueezing transform for seismic data analysis

Time-frequency methods, which allow us to observe the seismic signal in time and frequency domains simultaneously, can efficiently discern the seismic response features of geological bodies in different frequency bands. In this paper, a newly developed time-frequency method named second order multi-synchrosqueezing transform (SMSST) is introduced to analyze seismic data. SMSST combines the second-order instantaneous frequency estimation and the iterative idea of multi-synchrosqueezing transform to approximate the true instantaneous frequency trajectory. It solves the problems of non-reassignment points and the sensitivity to noise at the same time. Synthetic example is employed to validate the superiority of SMSST in time-frequency analysis. Results obtained from four different methods show that SMSST offer the best performance in terms of energy-concentration and noise robustness. Applications on field data further demonstrate that SMSST-based method is suitable and effective to highlight geological information and stratigraphic features compared to the previous techniques. The capabilities of SMSST for accurate reservoir localization with high resolution, making it a promising and potential tool in seismic interpretation.

Comparative study of time-frequency transformation methods for ECG signal classification

In this study, we highlighted the growing need for automated electrocardiogram (ECG) signal classification using deep learning to overcome the limitations of traditional ECG interpretation algorithms that can lead to misdiagnosis and inefficiency. Convolutional neural networks (CNN) application to ECG signals is gaining significant attention owing to their exceptional image-classification capabilities. However, we addressed the lack of standardized methods for converting 1D ECG signals into 2D-CNN-compatible input images by using time-frequency methods and selecting hyperparameters associated with these methods, particularly the choice of function. Furthermore, we investigated the effects of fine-tuned training, a technique where pre-trained weights are adapted to a specific dataset, on 2D-CNNs for ECG classification. We conducted the experiments using the MIT-BIH Arrhythmia Database, focusing on classifying premature ventricular contractions (PVCs) and abnormal heartbeats originating from ventricles. We employed several CNN architectures pre-trained on ImageNet and fine-tuned using the proposed ECG datasets. We found that using the Ricker Wavelet function outperformed other feature extraction methods with an accuracy of 96.17%. We provided crucial insights into CNNs for ECG classification, underscoring the significance of fine-tuning and hyperparameter selection in image transformation methods. The findings provide valuable guidance for researchers and practitioners, improving the accuracy and efficiency of ECG analysis using 2D-CNNs. Future research avenues may include advanced visualization techniques and extending CNNs to multiclass classification, expanding their utility in medical diagnosis.

Time-varying modal identification of structures under seismic excitations using a novel time-frequency method

Civil engineering structures are susceptible to damage when subjected to seismic excitations, resulting in presenting nonlinear features and exhibiting time-varying dynamic behavior of structural modal properties. The instantaneous frequency (IF) of structures is thus an essential indicator to evaluate structural damage state. Time-varying filtering empirical mode decomposition (TVF-EMD) holds promise for non-stationary signals decomposition and IF identification due to its robustness against noise interference. However, the application of TVF-EMD is limited by the requirement for manually presetting the decomposition parameters (i.e., B-spline order and bandwidth threshold). In this study, a novel IF identification method based on an improved TVF-EMD algorithm is proposed. In this method, TVF-EMD is firstly improved to accurately decompose the measured responses into mono-component modal responses, which adopts orthogonal coefficient and energy kurtosis as the objective function of salp swarm algorithm (SSA) to adaptively determine the optimal decomposition parameters. Then, the resulting mono-component modal responses are analyzed by local maximum synchrosequencing transform (LMSST) to obtain structural IF under seismic excitations. Examples of non-stationary signals of sinusoidal function, Duffing system, and simulated two-story shear building model under El Centro seismic excitations are used to illustrate the advantages of the proposed method, which proves to be successful in signal decomposition and IF identification. Furthermore, the proposed method is applied to a shaking table test and a real building-Van Nuys hotel under seismic excitations to identify their IF and evaluate structural damage states. The results reveal that the proposed method is efficient for structural IF identification, and can be utilized to qualitatively evaluate the damage severity of structures subjected to strong seismic excitations.

Nonstationary time-frequency characteristics of vehicle suspension systems based on evolutionary power spectral density

Improving the ride comfort for vehicles that travel at varying speeds is a nonstationary problem and has been an increasingly important topic for suspension system research. Accurate identification of frequencies associated with the resonant responses is needed for effective design of active suspension control strategies. However, traditional time-frequency (TF) methods have resolution limitations in either the time domain or the frequency domain. This paper proposes a new methodology to employ the evolutionary power spectral density (EPSD) to describe the responses of vehicles in the time-frequency domain. The key to calculate the responses in nonstationary cases is to derive the nonuniform modulation function which is obtained by the pseudo excitation method. To illustrate the applicability of the proposed method, an example of a seven-degree-of-freedom vehicle model is investigated in which the nonstationary excitations acting on the wheels are computed by the nonuniform modulation function and a precise integration method. Results show that resolutions obtained by the EPSD are more precise than the traditional TF methods with less than 0.2 Hz of bandwidth in both the lower frequency range at the first natural frequency of 1 Hz and in the higher frequency around 10 Hz. Moreover, the changing of the resonant frequency with varying speeds provides the insights, from the perspective of human body’s sensitivity to frequencies of vibration, to improve the ride comfort for vehicles under nonstationary driving conditions.

Ultrasonic velocity measurements of backscattered acoustic waves for monitoring the enzymatic coagulation of milk

In this work, the milk coagulation process was monitored by a nondestructive ultrasonic technique. Three analysis methods were used to calculate ultrasonic wave velocity and assess their effectiveness in tracking the physicochemical changes: Cross-correlation, Spectrum ratio, and Smoothed Pseudo-Wigner-Ville transform. The obtained results show a consistency between the velocity measurements made by these three methods, with a steady increase observed during coagulation and both phases are visible. The time-frequency method was most effective, showing a clearer transition between the two phases. This study suggests that non-destructive ultrasonic techniques with time-frequency analysis could be advantageous for monitoring milk coagulation and ensuring dairy product quality.

Application of synchro spline-kernelled chirplet transformation in nonlinear ultrasonic wave modulation: self-sensing method with temperature protection

The purpose of this work is to investigate the synchro spline-kernelled chirplet extracting transformation (SSCET) method for defect detection in the nonlinear ultrasonic wave modulation (NUWM) method. To implement the NUWM method using only one piezoelectric transducer, the self-sensing method is used. Self-sensing has many advantages, but it is sensitive to temperature changes. To reduce the temperature effects, a novel circuit has been designed and implemented. A sandwich beam with bolt loosening and an aluminum beam with boundary loosening damages are used to test the results of the SSCET method on the signal received from the self-sensing circuit. First, an aluminum beam with a loosened boundary is modeled based on beam theory including self-sensing circuits with temperature effects. In this study, SSCET results are compared with those of other time–frequency methods for the detection of the loosened boundary. Based on the temperature effects, the theoretical results are compared with the experimental results of the circuit. To quantify defect detection, a damage index calculated based on instantaneous frequency is provided. Three piezoelectric configurations are also compared with the self-sensing method damage index results. SSCET is then used to check bolt loosening in a sandwich beam for further investigation. The proposed method is compared to a previous self-sensing temperature compensation method. Based on the SSCET method, the severity of the bolt loosening is determined.