Time-Frequency analysis for wiring soft faults detection

This paper is to analyze and identify damage in gear teeth and rolling element bearings by establishing pattern feature parameters from vibration signatures. In the present work, different damage scenarios involving different combinations of gear tooth damage, bearing damage are considered. Each of the damage scenarios are studied and compared in the time domain, the frequency domain, and the joint time-frequency domain using the FM0 technique, the Fourier Transform, the Wigner-Ville Transform, and the Continuous Wavelet Transform, respectively. Results obtained from the three different signal domains are analyzed to develop indicative parameters and visual presentations that measure the integrity and wellness of the bearing and gear components. The joint time-frequency domain obtained from the continuous wavelet transform has shown to be a superior technique for providing clear visual examination solution for different types of component damages as well as for feature extractions used for computer-based machine health monitoring solution.

P01-Comparison of short-time Fourier transform and continuous wavelet transform for frequency analysis of sleep EEG

In this work, we describe different configurations of optical fiber interferometers (types Michelson and Mach-Zehnder) used to measure velocities during dynamical material's behaviour studies. We detail the algorithms of processing developed and optimized to improve the performance of these interferometers especially in terms of time and frequency resolutions. Three methods of analysis of interferometric signals were studied. For Michelson interferometers, the time-frequency analysis of signals by Short-Time Fourier Transform (STFT) is compared to a time-frequency analysis by Continuous Wavelet Transform (CWT). The results have shown that the CWT was more suitable than the STFT for signals with low signal-to-noise, and low velocity and high acceleration areas. For Mach-Zehnder interferometers, the measurement is carried out by analyzing the phase shift between three interferometric signals (Triature processing). These three methods of digital signal processing were evaluated, their measurement uncertainties estimated, and their restrictions or operational limitations specified from experimental results performed on a pulsed power machine.

Experimental study on supersonic combustion fluctuation using thin-film thermocouple and time–frequency analysis

Frequency domain analyses in electromyographic (EMG) signals are frequently applied to assess muscle fatigue and similar variables. Moreover, Fourier-based approaches are typically used for investigating these procedures. Nonetheless, Fourier analysis assumes the signal as stationary which is unlikely during dynamic contractions. As an alternative method, wavelet-based treatments do not assume this pattern and may be considered as more appropriate for joint time-frequency domain analysis. Based on the previous statements, the purpose of the present study was to compare the application of Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) to assess muscle fatigue in dynamic exercise of a 1-km of cycling (time-trial condition). The results of this study indicated that CWT and STFT analyses have provided similar fatigue estimates (slope) (p> 0.05). However, CWT application represents lesser dispersion (pp> 0.05) according to different methods, it is important to note that these responses seem to show greater values for CWT compared to STFT for 2 superficial muscles. Thereby, we are capable of considering CWT as a reliable and useful method to take into consideration when non-stationary or oscillating exercise models are evaluated.

Frequency domain analyses of changes in electromyographic (EMG) signals over time are frequently used to assess muscle fatigue. Fourier based approaches are typically used in these analyses, yet Fourier analysis assumes signal stationarity, which is unlikely during dynamic contractions. Wavelet based methods of signal analysis do not assume stationarity and may be more appropriate for joint time-frequency domain analysis. The purpose of this study was to compare Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) in assessing muscle fatigue in supramaximal constant load dynamic exercise (110% VO(2peak)). The results of this study indicate that CWT and STFT analyses give similar fatigue estimates (slope of median frequency) in supramaximal constant load dynamic exercise (P>0.05). However, the results of the variance was significantly lower for at least one of the muscles studied in CWT compared to STFT (P < 0.05) indicating more variability in the EMG signal analysis using STFT. Thus, the stationarity assumption may not be the sole factor responsible for affecting the Fourier based estimates.

Epilepsy is one of the most common neurological disorders. Epileptic seizures are the manifestation of abnormal hypersynchronous discharges of cortical neurons that impair brain function. Most of the people affected can be treated successfully with drug therapy or neurosurgical procedures. But there is still a large group of epilepsy patients that continues to have frequent seizures. For these patients automated detection of epileptic seizures can be of great clinical importance. Seizure detection can influence daily care or can be used to evaluate treatment effect. Furthermore automated detection can be used to trigger an alarm system during seizures that might be harmful to the patient. This thesis focusses on accelerometry (ACM) based seizure detection. A detailed overview is provided, on the perspectives for long-term epilepsy monitoring and automated seizure detection. The value of accelerometry for seizure detection is shown by means of a clinical evaluation and the first steps are made towards automatic detection of epileptic seizures based on ACM. With accelerometers movements are recorded. A large group of epileptic seizures manifest in specific movement patterns, so called motor seizures. Chapter 2 of this thesis presents an overview of the published literature on available methods for epileptic seizure detection in a long-term monitoring context. Based on this overview recommendations are formulated that should be used in seizure detection research and development. It is shown that for seizure detection in home environments, other sensor modalities besides EEG become more important. The use of alternative sensor modalities (such as ACM) is relatively new and so is the algorithm development for seizure detection based on these measures. It was also found that for both the adaptation of existing techniques and the development of new algorithms, clinical information should be taken more into account. The value of ACM for seizure detection is shown by means of a clinical evaluation in chapter 3. Here 3-D ACM- and EEG/video-recordings of 18 patients with severe epilepsy are visually analyzed. A striking outcome presented in this chapter is the large number of visually detected seizures versus the number of seizures that was expected on forehand and the number of seizures that was observed by the nurses. These results underscore the need for an automatic seizure detection device even more, since in the current situation many seizures are missed and therefore it is possible that patients do not get the right (medical) treatment. It was also observed that 95% of the ACM-patterns during motor seizures are sequences of three elementary patterns: myoclonic, tonic and clonic patterns. These characteristic patterns are a starting point for the development of methods for automated seizure detection based on ACM. It was decided to use a modular approach for the detection methodology and develop algorithms separately for motor activity in general, myoclonic seizures and tonic seizures. Furthermore, clinical information is incorporated in the detection methodology. Therefore in this thesis features were used that are either based on the shape of the patterns of interest as described in clinical practice (chapter 4 and 7), or the features were based on a physiological model with parameters that are related to seizure duration and intensity (chapter 5 and 6). In chapter 4 an algorithm is developed to distinguish periods with and without movement from ACM-data. Hence, when there is no movement there is no motor seizure. The amount of data that needs further analysis for seizure detection is thus reduced. From 15 ACM-signals (measured on five positions on the body), two features are computed, the variance and the jerk. In the resulting 2-D feature space a linear threshold function is used for classification. For training and testing the algorithm ACM data along with video data are used from nocturnal recordings in mentally retarded patients with severe epilepsy. Using this algorithm the amount of data that needs further analysis is reduced considerably. The results also indicate that the algorithm is robust for fluctuations across patients and thus there is no need for training the algorithm for each new patient. For the remaining data it needs to be established whether the detected movement is seizure related or not. To this purpose a model is developed for the accelerometer pattern measured on the arm during a myoclonic seizure (chapter 5). The model consists of a mechanical and an electrophysiological part. This model is used as a matched wavelet filter to detect myoclonic seizures. In chapter 6 the model based wavelet is compared to three other time frequency measures: the short time Fourier transform, the Wigner distribution and the continuous wavelet transform using a Daubechies wavelet. All four time-frequency methods are evaluated in a linear classification setup. Data from mentally retarded patients with severe epilepsy are used for training and evaluation. The results show that both wavelets are useful for detection of myoclonic seizures. On top of that, our model based wavelet has the advantage that it consists of parameters that are related to seizure duration and intensity that are physiological meaningful. Besides myoclonic seizures, the model is also useful for the detection of clonic seizures; physiologically these are repetitive myoclonic seizures. Finally for the detection of tonic seizures, in chapter 7 a set of features is studied that incorporate the mean characteristics of ACM-patterns associated with tonic seizures. Linear discriminant analysis is used for classification in the multi-dimensional feature space. For training and testing the algorithm, again data are used from recordings in mentally retarded patients with severe epilepsy. The results show that our approach is useful for the automated detection of tonic seizures based on 3-D ACM and that it is a promising contribution in a complete multi-sensor seizure detection setup.

Aiming reliable detection and localization of cerebral blood flow and emboli, embolic signals were added to simulated middle cerebral artery Doppler signals and analysed. Short-time Fourier transform (STFT) and continuous wavelet transform (CWT) were used in the evaluation. The following parameters were used in this study: the powers of the embolic signals added were 5, 6, 6.5, 7, 7.5, 8 and 9 dB; the mother wavelets for CWT analysis were Morlet, Mexican hat, Meyer, Gaussian (order 4) and Daubechies (orders 4 and 8); and the thresholds for detection (equated in terms of false positive, false negative and sensitivity) were 2 and 3.5 dB for the CWT and STFT, respectively. The results indicate that although the STFT allows accurately detecting emboli, better time localization can be achieved with the CWT. Among the CWT, the current best overall results were obtained with Mexican Hat mother wavelet, with optimal results for sensitivity (100% detection rate) for nearly all emboli power values studied.

A voice is a sound which is created by vibration of the vocal cords, which means that, the vocal cords approach to each other by passing the air through the larynx and followed by different sounds. This vibration is under the influence of the statuses of tongue, teeth and lips, as well as the other effective factors. This vibrating air causes some minor changes around the individual speaker, which is called the voice. Some of the most important procedures in the voice signal analyzing is the signal processing methods in frequency and time-frequency domains; the most conventional approach in frequency domain is the Fast Fourier Transform (FFT) method, on the other hand the time-frequency signal processing methods can identify the frequency components of the signal and extract its time-varying characteristics; moreover they are effective tools for extracting the information of non-stationary signals. Time-frequency analysis methods can be classified into linear and nonlinear categories. The Short-Time Fourier Transform and the Wavelet Transform are the most conventional linear methods. This paper investigates the differences in the energy levels of explosive consonants in voiced mode and unvoiced mode using the most conventional frequency analysis and linear time-frequency analysis methods; these approaches are very effective and profitable in phonetic science and biomedical engineering science in order to diagnosing and determining the severity of laryngeal diseases and brain injuries. Results of this study indicate that the energy level of explosive consonants in voiced mode is more than unvoiced mode; also using Fast Fourier and Wavelet Transforms presents the results in better resolution and better image quality than the short-time Fourier Transform.

BackgroundTime-Frequency analysis of electroencephalogram (EEG) during different mental tasks received significant attention. As EEG is non-stationary, time-frequency analysis is essential to analyze brain states during different mental tasks. Further, the time-frequency information of EEG signal can be used as a feature for classification in brain-computer interface (BCI) applications.MethodsTo accurately model the EEG, band-limited multiple Fourier linear combiner (BMFLC), a linear combination of truncated multiple Fourier series models is employed. A state-space model for BMFLC in combination with Kalman filter/smoother is developed to obtain accurate adaptive estimation. By virtue of construction, BMFLC with Kalman filter/smoother provides accurate time-frequency decomposition of the bandlimited signal.ResultsThe proposed method is computationally fast and is suitable for real-time BCI applications. To evaluate the proposed algorithm, a comparison with short-time Fourier transform (STFT) and continuous wavelet transform (CWT) for both synthesized and real EEG data is performed in this paper. The proposed method is applied to BCI Competition data IV for ERD detection in comparison with existing methods.ConclusionsResults show that the proposed algorithm can provide optimal time-frequency resolution as compared to STFT and CWT. For ERD detection, BMFLC-KF outperforms STFT and BMFLC-KS in real-time applicability with low computational requirement.

This paper presents a novel method for EEG channel selection based on the Hellinger Distance (HD) computed over time–frequency representations (TFRs). Here, we first convert raw EEG into the time–frequency domain using Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT). Leveraging Hellinger Distance, we then identify and remove outlier epochs via a z-score threshold, and rank and select the most discriminative channels by measuring how well each channel’s TFR distributions separate different classes. Our empirical evaluation uses the BCI Competition IVa dataset to compare the proposed HD-based approach (HD-CSP) against multiple variants of the Common Spatial Pattern algorithm, including standard CSP, L1 Norm CSP, SCSP, FBCSP, and E-CSP. Results indicate that HD-CSP consistently outperforms competing methods in all tested configurations, achieving notably high classification accuracy even when the number of channels is severely restricted. In particular, HD-CSP reaches around 70\% accuracy with only three channels, while other approaches suffer significant performance drops. As the number of channels increases, HD-CSP maintains its superior accuracy, exceeding 80% in some configurations. Overall, the proposed method is superior on performance gains and ability to adapt to diverse channel configurations suggest broad applicability, especially in resource-constrained EEG settings where efficiency and accuracy are both priorities.

The monitoring of the evolution of structural dynamic response under transient loads must be carried out to understand the physical behaviour of building subjected to earthquake ground motion, as well as to calibrate numerical models simulating their dynamic behaviour. Fourier analysis is one of the most used tools for estimating the dynamic characteristics of a system. However, the intrinsic assumption of stationarity of the signal imposes severe limitations upon its application to transient earthquake signals or when the dynamic characteristics of systems change over time (e.g., when the frequency of vibration of a structure decreases due to damage). Some of these limitations could be overcome by using the Short Time Fourier Transform (STFT). However, the width of the moving window adopted for the analysis has to be fixed as a function of the minimum frequency of interest, using the best compromise between resolution in both the time and frequency domains. Several other techniques for time-frequency analysis of seismic signals recorded in buildings have been recently proposed. These techniques are more suitable than the STFT for the application described above, although they also present drawbacks that should be taken into account while interpreting the results. In this study, we characterize the dynamic behaviour of the Falkenhof Tower (Potsdam, Germany) while forced by ambient noise and vibrations produced by an explosion. We compare the results obtained by standard frequency domain analysis with those derived by different time-frequency methods. In particular, the results obtained by the standard Transfer Function method, Horizontal to Vertical Spectral Ratio (HVSR), Short Time Fourier Transform (STFT), Empirical Mode Decomposition (EMD) and S-Transform are discussed while most of the techniques provide similar results, the EMD analyses suffer some problems derived from the mode mixing in most of the Intrinsic Mode Functions (IMFs).

Time-frequency (TF) characterization of electromyographic (EMG) bursts is essential for accurately assessing muscle function, particularly when the signals exhibit a high degree of nonstationarity. In this exploratory study, we investigated the temporal dynamics of the spectral components associated with short-latency EMG bursts using several TF analysis techniques. Specifically, we compared the performance and interpretability of spectrograms obtained via the short-time Fourier transform (STFT), the continuous wavelet transform (CWT), and noise-assisted multivariate empirical mode decomposition (NA-MEMD), applied to EMG signals recorded from the biceps femoris muscle of freely moving rats in an animal model of Parkinson's disease, acquired using chronically implanted bipolar electrodes during treadmill locomotion. For each method, we evaluated its effectiveness in capturing transient variations in frequency content, the stability of extracted features across bursts, and the extent to which these features reflect physiologically meaningful aspects of muscle activation. The results show that TF approaches reveal complementary information about burst structure; NA-MEMD provides greater adaptability to nonlinear and nonstationary components, whereas STFT- and CWT-based representations offer more controlled and comparable analyses. Overall, these findings highlight the value of TF analysis as a methodological tool for evaluating muscle function and provide a solid foundation for selecting analytical strategies in studies where EMG bursts exhibit complex and highly variable spectral profiles.

In field harvesting conditions, the non-stationary random vibration characteristics of the harvester are rarely considered, and the results of vibration frequency calculated by different time–frequency transformation methods are different. In this paper, the harvester’s vibration characteristics under the time-varying mass were studied, and the correlation between vibration frequency and modal frequency was analyzed. Firstly, under the conditions of time-varying mass (field harvesting conditions) and non-time-varying mass (empty running condition), the non-stationarity characteristics of vibration signals at 16 measurement points of a combined corn harvester frame were studied. Then, fast Fourier transform (FFT), short-time Fourier transform (STFT), and continuous wavelet transform (CWT) were used to calculate the vibration frequency distribution characteristics of the corn harvester. Finally, based on the EFDD (enhanced frequency domain decomposition) algorithm, the correlation between the primary vibration frequency and the operating mode frequency is studied. The results show that the mean, variance, and maximum difference of the vibration amplitude under harvesting conditions (mass time-varying system) are 0.10, 26.5, and 1.0, respectively, at different harvesting periods (0~10 s, 10~20 s, 20~30 s). The harvesting conditions’ vibration signals conform to the characteristics of non-stationary randomness. The FFT algorithm is used to obtain more dense vibration frequencies, while the frequencies based on STFT and CWT algorithms are sparse. The correlation between the FFT method and the EFDD algorithm is 0.98, and the correlation between the STFT, CWT, and the EFDD algorithm is 0.99 and 0.98. Therefore, the primary frequency of the STFT methods is closer to the modal frequency. Our research laid the foundation for further study and application of mass time-varying combined harvester system non-stationary random vibration modal frequency identification and vibration control.

The short time Fourier transform (STFT) cannot resolve rapid velocity changes in most photonic Doppler velocimetry (PDV) data. A practical analysis method based on the continuous wavelet transform (CWT) was presented to overcome this difficulty. The adaptability of the wavelet family predicates that the continuous wavelet transform uses an adaptive time window to estimate the instantaneous frequency of signals. The local frequencies of signal are accurately determined by finding the ridge in the spectrogram of the CWT and then are converted to target velocity according to the Doppler effects. A performance comparison between the CWT and STFT is demonstrated by a plate-impact experiment data. The results illustrate that the new method is automatic and adequate for analysis of PDV data.