“Drive-by’’ bridge frequency-based monitoring utilizing wavelet transform

The fast Fourier transform (FFT) algorithm is widely used as a standard tool to carry out spectral analysis because of its computational efficiency. However, the presence of multiple tones frequently requires a fine frequency resolution to achieve sufficient accuracy, which imposes the use of a large number of FFT points that results in large area and power overheads. In this paper, an FFT method is proposed for on-chip spectral analysis of multi-tone signals with particular harmonic and intermodulation components. This accurate FFT analysis approach is based on coherent sampling, but it requires a significantly smaller number of points to make the FFT realization more suitable for on-chip built-in testing and calibration applications that require area and power efficiency. The technique was assessed by comparing the simulation results from the proposed method of single and multiple tones with the simulation results obtained from the FFT of coherently sampled tones. The results indicate that the proper selection of test tone frequencies can avoid spectral leakage even with multiple narrowly spaced tones. When low-frequency signals are captured with an analog-to-digital converter (ADC) for on-chip analysis, the overall accuracy is limited by the ADC's resolution, linearity, noise, and bandwidth limitations. Post-layout simulations of a 16-point FFT showed that third-order intermodulation (IM3) testing with two tones can be performed with 1.5-dB accuracy for IM3 levels of up to 50 dB below the fundamental tones that are quantized with a 10-bit resolution. In a 45-nm CMOS technology, the layout area of the 16-point FFT for on-chip built-in testing is 0.073 mm2, and its estimated power consumption is 6.47 mW.

Fourier and wavelet analyses for fatigue assessment of concrete beams

Abstract. Several magnetic measurements and theoretical developments from different research groups have shown certain relationships with worldwide geological processes. Secular variation in geomagnetic cutoff rigidity, magnetic frequencies, or magnetic anomalies have been linked with spatial properties of active convergent tectonic margins or earthquake occurrences during recent years. These include the rise in similar fundamental frequencies in the range of microhertz before the Maule 2010, Tōhoku 2011, and Sumatra–Andaman 2004 earthquakes and the dramatic rise in the cumulative number of magnetic anomalous peaks before several earthquakes such as Nepal 2015 and Mexico (Puebla) 2017. Currently, all of these measurements have been physically explained by the microcrack generation due to uniaxial stress change in rock experiments. The basic physics of these experiments have been used to describe the lithospheric behavior in the context of the seismo-electromagnetic theory. Due to the dramatic increase in experimental evidence, physical mechanisms, and the theoretical framework, this paper analyzes vertical magnetic behavior close to the three latest main earthquakes in Chile: Maule 2010 (Mw 8.8), Iquique 2014 (Mw 8.2), and Illapel 2015 (Mw 8.3). The fast Fourier transform (FFT), wavelet transform, and daily cumulative number of anomalies methods were used during quiet space weather time during 1 year before and after each earthquake in order to filter space influence. The FFT method confirms the rise in the power spectral density in the millihertz range 1 month before each earthquake, which decreases to lower values some months after earthquake occurrence. The cumulative anomaly method exhibited an increase prior to each Chilean earthquake (50–90 d prior to earthquakes) similar to those found for Nepal 2015 and Mexico 2017. The wavelet analyses also show similar properties to FFT analysis. However, the lack of physics-based constraints in the wavelet analysis does not allow conclusions that are as strong as those made by FFT and cumulative methods. By using these results and previous research, it could be stated that these magnetic features could give seismic information about impending events. Additionally, these results could be related to the lithosphere–atmosphere–ionosphere coupling (LAIC effect) and the growth of microcracks and electrification in rocks described by the seismo-electromagnetic theory.

This paper presents a review of the researches done on fault tolerant control types, methods, main objectives of the fault tolerant control and fault diagnosis of induction motor faults that used the wavelet transform. Wavelet transform from the fault diagnosis point of view, is a summary of the wavelet types (continuous and discrete), machine faults, diagnosis methods and their validation, respectively. Types of software, generality of codes, one dimensional and two dimensional DWT and frequency characteristics components of healthy and faulty induction motor are given. Finally, stator short winding and open winding are taken as a case study to show the effectiveness of the wavelet techniques for fault diagnosis. Key words: Wavelet, induction motor, fault diagnosis, fast Fourier transform, fault indicator, fault tolerant control.

This paper deals with an indirect health monitoring strategy for bridges using an instrumented vehicle. Thermodynamic principles are used to relate the change in Vehicle–Bridge-Interaction (VBI) forces to the change in dynamic tyre pressure. The damage identification process involves two stages. In the first stage, the unknown tyre model parameters are estimated using Bayesian inference based on the calibration data. The approach uses a Stein variational gradient descent implementation of the Bayes rule to quantify the uncertainty in the estimated tyre parameters. In the second stage, the calibrated tyre model is used to reconstruct the change in VBI force from measured tyre pressure data considering a damaged bridge. It is observed that damage present in the bridge produces notable changes in VBI force. Contour plots based on VBI force and natural frequency are developed for damage detection. The reconstructed VBI force change is used to quantify damage using the contour plots. Further, the least square estimation approach is adopted for damage identification by defining appropriate objective functions and imposing constraints on the damage indicators. The damage is estimated by minimizing the objective function using Cuckoo search algorithm. Numerical experiments reveal that the developed method could be used for accurate damage identification in the presence of measurement noise, uncertainty in estimated tyre parameters, and the uncertainty in bridge model parameters.

Non-invasive autonomic evaluation has used fast Fourier transform (FFT) to assign a range of low (LF) and high frequencies (HF) as markers of sympathetic and parasympathetic influences, respectively. However, FFT cannot be applied to brief transient phenomena, such as those observed on performing autonomic tests where the acute changes of cardiovascular signals (blood pressure and heart rate) that represent the first and most important stage of the autonomic performance towards a new state of equilibrium occur. Wavelet analysis has been proposed as a method to overcome and complement information taken exclusively in the frequency domain. With discrete wavelet transform (DWT), a time-frequency analysis can be done, allowing the visualization in time of the contribution of LF and HF to the observed changes of a particular signal. In this study, we evaluate with wavelets the acute changes in R-R intervals and systolic blood pressure that are observed in normal subjects during four classical autonomic tests: head-up tilt (HUT), cold pressor test (CPT), deep breathing (DB) and Valsalva manoeuvre (VM). Continuous monitoring of ECG and blood presure was performed. Also LF, HF and LF/HF were calculated. Consistent with previous interpretations, data showed an increase of sympathetic activity in HUT, CPT and VM. On DB, results reflected an increase in parasympathetic activity and frequencies. In conclusion, when compared with FFT, wavelet analysis allows the evaluation of autonomic variability during short and non-stationary periods of time and may constitute a useful advance in the assessment of autonomic function in both physiological and pathological conditions.

This research investigates the dynamic behavior of a railway bridge using both experimental and numerical methods. Field tests were conducted to capture the bridge response to live loading conditions with acceleration data collected via uniaxial accelerometers placed at critical locations along the structure. The dynamic characteristics, including the natural frequencies and mode shapes, were determined using two analytical techniques: Fast Fourier Transform (FFT) and Operational Modal Analysis (OMA). While FFT provides a frequency domain analysis, OMA enables the estimation of modal parameters, such as natural frequencies, mode shapes, and damping ratios, using the bridge's response to operational forces. The results revealed that the fundamental frequency obtained from the OMA (2.163 Hz) was higher than that obtained from the FFT (1.95 Hz) and the Finite Element Analysis (FEA) model (1.65 Hz). Additionally, the OMA produced mode shapes that were closely aligned with those predicted by the FEA, validating the accuracy of the numerical model. This study highlights the advantages of OMA over FFT, particularly the ability to capture mode shapes, and underscores the importance of integrating OMA with FEA for a comprehensive dynamic assessment of bridge structures. These findings contribute to the growing body of knowledge on structural monitoring and provide practical insights into improving bridge safety and performance.

Unsupervised learning-based framework for indirect structural health monitoring using adversarial autoencoder

The Fast Wavelet Transform (FWT) is a powerful new tool which can be used for vibration analysis and condition monitoring of advanced rotating machinery. The main advantage of wavelet analysis for condition monitoring is that so-called wavelet maps can be produced showing three dimensional plots of amplitude versus frequency and time. This is in contrast to Fast Fourier Transform (FFT) analysis, in which the time domain of the signal is lost. The wavelet maps provide striking visual indications of tiny changes in machine behaviour which cannot be detected in a normal frequency spectrum. This improves the chances of averting catastrophic failures and expands the time window available to take corrective action. Additional advantages of wavelet analysis over FFT analysis include: (1) no requirements for periodicity of the signal, (2) extremely fast computation, (3) the location of patterns in the time domain and (4) an effective detection of high frequency details. Wavelet analyses of all types are available but user-friendly information is hard to come by and this has a detrimental effect on progress towards practical commercial applications. Thus, the main purpose of this paper is to provide a simple and clear introduction to wavelet analysis and its use in machine condition monitoring. The paper has been written for an audience having some familiarity with spectrum analysis but no prior knowledge of wavelets.

Vibration-induced fatigue failure is a prevalent and critical damage mechanism in wing rib–beam structures operating under complex loading and harsh service environments. Accurate characterization of their dynamic properties is essential for enhancing structural safety and reliability. Strain modal analysis, recognized as a powerful tool for structural health monitoring (SHM) and early damage detection, shows significant potential in high-performance aerospace applications. Fiber Bragg Grating (FBG) sensors, owing to their compact size, low weight, immunity to electromagnetic interference, and high multiplexing capability, are particularly advantageous for capturing dynamic strain responses in complex structural configurations. This work presents an integrated frequency identification approach that combines distributed FBG sensing with two complementary frequency-domain techniques: Fast Fourier Transform (FFT) and Multiple Signal Classification (MUSIC). FFT is applied to rapidly and intuitively identify dominant single-frequency excitation components, while MUSIC provides high-resolution separation of closely spaced modal frequencies and precise extraction of modal parameters. The methodology is first implemented on a full-scale wing rib–beam structure to simultaneously identify excitation and natural frequencies. It is further validated through controlled experiments and finite element simulations on a representative cantilever beam. Experimental results demonstrate that the combined FFT–MUSIC framework achieves accurate and efficient identification of both excitation and natural frequencies. The frequencies and strain mode shapes obtained from the FBG system exhibit excellent agreement with those measured by conventional accelerometers and predicted by numerical models, confirming high accuracy and repeatability. The proposed method offers a robust and scalable solution for dynamic performance monitoring and vibration fatigue assessment of aerospace structures under complex service conditions.

Quickly accessing the contents of a video is challenging for users, particularly for unstructured video, which contains no intentional shot boundaries, no chapters, and no apparent edited format. We approach this problem in the domain of lecture videos though the use of machine learning, to gather semantic information about the videos; and through user interface design, to enable users to fully utilize this new information. First, we use machine learning techniques to gather the semantic information. We develop a system for rapid automatic semantic tagging using a heuristic-based feature selection algorithm called Sort-Merge, by using large initial heterogeneous low-level feature sets (cardinality greater than 1K). We explore applying Sort-Merge to heterogeneous feature sets though two methods: early fusion and late fusion. Each takes different approaches to handling the different kinds of features in the heterogeneous set. We determine the most predictive feature sets for key-frame filters such as “has text”, “has computer source code”, or “has instructor motion”. Specifically we explore the usefulness of Harr Wavelets, Fast Fourier Transforms, Color Coherence Vectors, Line Detectors, Ink Features and Pan/Tilt/Zoom detectors. For evaluation, we introduce a “keeper” heuristic for feature sets, which provides a method of performance comparison against a baseline. Second, we create a user interface to allow the user to make use of the semantic tags we gathered though our computer vision and machine learning process. The interface is integrated into an existing video browser, which detected shot-like boundaries and presented a multitimeline view. The content within shot-like boundaries is represented by frames to which our new interface applies the generated semantic tags. Specifically, we make accessible the semantic concepts of 'text', 'code', 'presenter', and 'person motion.' The tags are detected in the simulated shots using the filters generated with our machine learning approach and are displayed to users using a user-customizable multi-timeline view. We also generate tags based on ASRgenerated transcripts that have been limited to the words provided in the index of the course text book. Each of these occurrences is aligned with the simulated shots. Each spoken word becomes a tag analogous to the visual concepts. A full Boolean algebra over the tags is provided to enable new composite tags such as 'text or code, but no presenter.' Finally, we quantify the effectiveness of our features and our browser through user studies, both observational and task driven. We find that users that use the full suite of tools performed a search task in 60% of the time of users without access to tags. We find that when users are asked to perform search tasks they follow a nearly fixed pattern of accesses, alternating between the use of tags and Keyframes, or between the use of Word Bubbles and the media player. Based on user behavior and feedback, we redesigned the interface to group spatially interface components that are used together, removed un-used components, and redesigned the display of Word Bubbles to match that of the Visual Tags. We found that users strongly preferred the Keyframe tool, as well as both kinds of tags. Users also either found the algebra very useful or not useful at all.

In the last several years, there has been a discernible increase in research devoted to developing innovative and complex composite materials. Because of their superior performance, especially in the aircraft industry, Fibre Metal Laminates (FML) and hybrid structures made of glass, aramid fibre, carbon, or aluminium are the most commonly used of these new technological commodities. Thus, free vibration analysis is the first step in the design of these structures. The current work examines the vibration behavior of a fiber-metal-laminate (FML) composite beam using numerical and experimental methods, a novel material for aircraft. This research series evaluated the bending natural vibration frequencies of the multi-walled carbon nanotube FML composite cantilevered beam. The Bruel and Kjaer (B and K) Fast Fourier Transform (FFT) analyzer with a PULSE platform was used in this study to find the intrinsic vibration frequencies of glass FML beams. Two parameters that investigated the dynamic behavior of the FML composite beam were the amount of MWCNT filler material and the beam's length. There was a reasonable agreement between the experimental and numerical results and the natural frequencies. The amount of MWCNT filler added to the glass fiber epoxy enhances the natural frequency of the FML composite cantilevered beam, according to both experimental and computational calculations. Furthermore, it was discovered that the vibration's inherent bending frequency decreases with the beam length.

A new apparatus for measuring the dynamic dividing error between hob and worktable in large gear hobbing machines is described in which a pair of small and high sensitive servoaccelerometers are mounted tangentially on a periphery of the large worktable, 180° apart, in order to detect the non-uniformity of rotation of the worktable. Two acceleration signals from the servo-accelerometers are added on the workthble, so as to be additive for the circumferential acceleration and null each other for the rectilinear acceleration of the worktable. After the circumferential acceleration signal transmitted with a telemeter is processed by a pulse signal from the rotary encoder attached to hob shaft in this apparatus, the dynamic dividing error can be obtained. In an experimental use with a large size (3.3 m worktable diameter) gear hobbing machine, the dynamic dividing error has been measured and recorded. By transforming the recorded analogue signal with an FFT (Fast Fourier Transform) analyzer and by consulting to the schematic drawing of the rotational transmission mechanism, specific parts in the mechanism have been identified that cause the dividing error. Also, by transforming the circumferential acceleration of the worktable during quick starting test with an FFT analyzer, rotational natural frequency of the worktable can be obtained easily.

The detection of defects in GRP lattice structures by vibration measurements

This study investigates the vibrational characteristics of multi-layered graphene sheets with variable thickness (VTGSs) by using molecular dynamics (MD) simulations. It is aimed to determine how the natural frequencies and vibration damping ratios of variable-thickness graphene change with respect to temperature. Atomistic models for six distinct geometries (1L, 3LT, 3LTB, 5LT, 5LTB, and 9LTB) were generated to analyze the influence of structural design and temperature on their natural frequencies. The simulations were performed using the Large-Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) with an AIREBO potential to represent interatomic carbon interactions. Natural frequencies of all atomistic models were extracted by applying the Fast Fourier Transform (FFT) method to the Velocity Autocorrelation Function (VACF) data obtained from the simulations. In addition, the analysis was conducted at three different temperatures: 250 K, 300 K, and 350 K. Key findings reveal that an increase in the number of graphene layers results in a decrease in the fundamental natural frequency due to the increased mass of the structure. Moreover, it was noted that natural frequencies decrease with increasing temperature. It is attributed to the reduction in structural rigidity at higher thermal energies. These results provide critical insights into how geometric and thermal variations affect the dynamic behavior of complex multi-layered graphene structures.