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Structural health monitoring using empirical mode decomposition and the Hilbert phase
Abstract
This paper discusses a new signal processing tool involving the use of empirical mode decomposition and its application to health monitoring of structures. Empirical mode decomposition is a time-series analysis method that extracts a custom set of basis functions to describe the vibratory response of a system. In conjunction with the Hilbert Transform, the empirical mode decomposition method provides some unique information about the nature of the vibratory response. In this paper, the method is used to process time-series data from a variety of 1-D structures with and without structural damage. Empirically derived basis functions are processed through the Hilbert–Huang Transform to obtain magnitude, phase, and damping information. This magnitude, phase, and damping information is later processed to extract the underlying incident energy propagating through the structure. This incident energy is also referred to as the dereverberated response of a structure. Using simple physics-based models of 1-D structures, it is possible to determine the location and extent of damage by tracking phase properties between successive degrees of freedom. This paper also presents experimental validation of this approach using a civil building model. Results illustrate that this new time-series method is a powerful signal processing tool that tracks unique features in the vibratory response of structures.
... However, Fourier analysis has several shortcomings, in particular for the analysis of bridge dynamics. Firstly, it is unable to accurately represent non-periodic functions, due to the fact that it is derived on the assumption that the signal to be transformed is periodic and of infinite length [11]. Another deficiency is that Fourier analysis requires linearity, which proves a challenge as available data are frequently from systems that are nonlinear [12]. ...
... Lastly, the frequency components are obtained from an average over the whole length of the signal. This is a challenge when analysing signals of a non-stationary system [11], as measured signals produced by structural damage are of a non-stationary nature [6]. This is also a challenge for signals that are short in duration, such as the impulse response of cracked beams [14], or signals resulting from the ‗drive-by' application [14], [15]. ...
... For the purposes of optimisation, it is useful to rewrite this expression as one sine wave rather than the sum of eight sine waves. This involves rewriting (11) as a vector whose magnitude is the signal amplitude and direction is the signal phase (12). ...
... Firstly, it is unable to accurately represent non-periodic functions, due to the fact that it is derived on the assumption that the signal to be transformed is periodic and of infinite length (Pines and Salvino, 2006). Another deficiency is that Fourier analysis requires linearity, which proves a challenge as available data are frequently from systems that are nonlinear (Huang et al., 1998). ...
... Lastly, the frequency components are obtained from an average over the whole length of the signal. This is a challenge when analysing signals of a nonstationary system (Pines and Salvino, 2006), as measured signals produced by structural damage are of a non-stationary nature (Staszewski and Robertson, 2007). This is also a challenge for signals that are short in duration, such as the impulse response of cracked beams (Kim and Melhem 2004), or signals resulting from the 'drive-by' application (Kim and Melhem, 2004;González et al., 2010b). ...
... Many bridge damage detection methods use Fourier analysis as the principal signalprocessing tool (Staszewski and Robertson, 2007). However, Fourier analysis has several shortcomings; it is unable to accurately represent non-periodic functions (Pines and Salvino 2006), non-stationary functions (Qian and Chen, 1999) and it requires linearity. This is a challenge as available data in the 'drive-by' context is from a nonlinear system (Huang et al., 1998), measured signals where structural damage is present are of a non-stationary nature (Staszewski and Robertson, 2007) and the signals are short in duration (Kim and Melhem, 2004). ...
In many countries, a significant number of bridges are approaching or have exceeded their original design life, while at the same time, traffic loads are steadily increasing. It is now a requirement in many developed countries to inspect bridge infrastructure in order to provide adequate maintenance planning and guarantee adequate levels of transport service and safety. In bridge health monitoring, the use of the vibration response of the bridge, to operational loads, is advantageous since it does not cause disruption to traffic flow. The concept is that damage will alter the stiffness, mass, or damping of the system, and that this change will alter the measured dynamic response of the structure. In recent years, larger bridges are being instrumented and monitored on an ongoing basis. This provides a high level of protection to the public and early warning if the bridge becomes unsafe. However, the process is laborious, time-consuming and often very expensive, requiring the installation of sensors and data acquisition electronics on the bridge. The aim of this thesis is to verify the feasibility of a novel alternative; ‘drive-by’ damage detection in bridges, a relatively low cost method consisting of the use of a moving vehicle at highway speeds fitted with sensors to monitor bridge condition.
Vehicle-bridge interaction (VBI) models are used in numerical simulations to test the effectiveness of using data gathered from a moving vehicle to identify damage in a bridge. Initially, changes in damping of the bridge are successfully detected by a truck-trailer vehicle model containing accelerometers. The Power Spectral Density (PSD) of the time-shifted acceleration differences between signals from two sensors are used as the damage indicator. Results for the drive-by system are found to be of similar quality to results for an accelerometer located on the bridge. Results also indicate that bridge damage can be detected quite effectively in the presence of up to a 0.5% difference in axle properties and in the presence of 10% noise in the overall vehicle properties.
Bridge damping has been reported to be sensitive to damage in concrete bridges, however it is unlikely to be effective for steel bridges and is also influenced by environmental phenomena. A crack modelled as a loss in stiffness over a length of beam, is therefore introduced as an alternative approach. This poses challenges in the drive-by application as the data collected is short in duration and standard signal processing techniques often fail to detect bridge information from the vehicle response. A novel algorithm is proposed that uses an optimisation approach as an alternative to standard signal processing techniques for the analysis of short signal segments in the drive-by application. Simulations using a model of a beam in free vibration show that modest losses of stiffness in the bridge can be detected using the vehicle measurements, even in the presence of significant noise levels.
Much of the research to date in the area of drive-by inspection uses two-axle cars or truck-trailer vehicle models, retrospectively fitted with sensors. The recently developed prototype ‘Traffic Speed Deflectometer’ (TSD) is capable of performing pavement deflection surveys at speeds of up to 80 km h-1, avoiding traffic disruption and expensive traffic management. The TSD is investigated here for bridge damage detection using a simply supported finite element beam as the bridge model. Three sensors are used and time-shifted curvatures are proposed as the novel damage indicator. Simulations show that modest local losses of stiffness in a beam can be detected using measurements from the TSD, even in the presence of realistic levels of noise. Differences in the transverse position of the vehicle on the bridge from one measurement to the next, are also investigated and its effect is shown to be insignificant.
Finally, the optimisation approach and the subtraction concept that have been developed are combined in simulations for damage detection in bridges using the TSD vehicle model. In numerical VBI simulations, this research is the first to investigate using the TSD in a drive-by bridge damage detection. An optimisation approach is used as an alternative to standard signal processing techniques to overcome the challenges of the short signal. Five different levels of damage are considered, and the approach allows for noise in the signal and variation in the transverse position of the vehicle in its track. Damage can be detected clearly, even for low levels of damage. For the first time, damage detection in bridges can be effectively carried out at highway speeds in the drive-by context, without contamination from the road profile, using just two sensors.
... The most common signal processing techniques that have been previously used in vibration-based studies are fast Fourier transform (FFT), 1 -5 short-time Fourier transform (STFT), 6,7 wavelet transform (WT), 8 -13 and Hilbert-Huang transform (HHT). 14 - 19 Although the classical fast Fourier spectral analysis method has a higher extraction efficiency than other algorithms, it has been shown that it is deficient in the processing of nonlinear and non-stationary signals. The traditional time-frequency analysis methods, such as STFTs, are basically the windowed Fourier transforms which can be used to analyze non-stationary signals and linear data. ...
... Xu and Chen 25 conducted an experimental investigation to detect and locate damage using the EMD method by applying abrupt changes in the structural stiffness of a three-story shear building. Pines and Salvino 14 proposed a signal processing method based on the processing of time-series data from a 1D scaled civil building, tested in the cases with and without structural damage. From the results, it was found that this method is capable to address the unique features of the vibratory response of the structure. ...
Signal processing is one of the essential components in vibration-based approaches and damage detection for structural health monitoring. Since signals in the real world are often nonlinear and non-stationary, especially in extended and complex structures, such as bridges, the Hilbert–Huang transform is used for damage assessment. In recent years, the empirical mode decomposition technique has been gradually used in structural health monitoring and damage detection. In this article, the application of complete ensemble empirical mode decomposition with adaptive noise technique is investigated to identify the presence, location, and severity of damage on a steel truss bridge model. The target is built at laboratory conditions and experimentally subjected to white noise excitations. By employing complete ensemble empirical mode decomposition with adaptive noise technique, four key features extracted from the intrinsic mode functions, including energy, instantaneous amplitude, unwrapped phase, and instantaneous frequency, are assessed to localization, quantification, and detection of damage both quantitatively and qualitatively. In addition, to further explore the sensitivity of the damage detection approach based on the complete ensemble empirical mode decomposition with adaptive noise technique method, several improved damage indices are proposed based on the combinations of two statistical time-history features, including kurtosis and entropy features with the energy and instantaneous amplitude features of the analyzed signal. The experimental results from the damage indices based on the extracted features demonstrate the robustness, superiority, and more sensitivity of the complete ensemble empirical mode decomposition with adaptive noise technique method in addressing the damage location, classifying the severity, and detecting the damage compared to empirical mode decomposition and ensemble empirical mode decomposition techniques.
... The procedure of this technique contains two steps: (i) to decompose the original signal by the empirical mode decomposition (EMD) method into a series of complete and oscillatory components, named intrinsic mode functions (IMFs), and (ii) to capture the instantaneous frequency and amplitude features by applying Hilbert transform (HT) to the IMFs. The vast majority of studies in the literature utilized HHT based on EMD for SHM and damage detection purposes [10][11][12][13][14][15][16]. ...
... Pines and Salvino [11] proposed a signal processing method based on the analysis of time-series data from a one-dimensional scaled civil building which was tested for the cases with and without structural damage. From the results, it was found that this method was able to address the unique features of the vibratory response of the structure. ...
Vibrations of complex structures such as bridges mostly present nonlinear and non-stationary behaviors. Recently, one of the most common techniques to analyze the nonlinear and non-stationary structural response is Hilbert–Huang Transform (HHT). This paper aims to evaluate the performance of HHT based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) technique using an Artificial Neural Network (ANN) as a proposed damage detection methodology. The performance of the proposed method is investigated for damage detection of a scaled steel-truss bridge model which was experimentally established as the case study subjected to white noise excitations. To this end, four key features of the intrinsic mode function (IMF), including energy, instantaneous amplitude (IA), unwrapped phase, and instantaneous frequency (IF), are extracted to assess the presence, severity, and location of the damage. By analyzing the experimental results through different damage indices defined based on the extracted features, the capabilities of the CEEMDAN-HT-ANN model in detecting, addressing the location and classifying the severity of damage are efficiently concluded. In addition, the energy-based damage index demonstrates a more effective approach in detecting the damage compared to those based on IA and unwrapped phase parameters.
... The time-frequency method involves decomposing the signal in both time and frequency domains. Time-frequency domain analysis methods mainly include the wavelet transform method, 11,12 empirical mode decomposition (EMD), 12 Hilbert-Huang transform method, 13,14 and so on. Continuous, in-depth examination of parameter recognition algorithms has facilitated ongoing development in the field of modal analysis. ...
Stochastic subspace identification (SSI) stands as one of the most extensively employed algorithms for modal parameter identification within the domain of bridge structural health monitoring. However, when confronted with nonstationary signals, it often generates numerous false modes in the stability graph, consequently impeding the accuracy of modal parameter identification. To address this challenge, an algorithm combining the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and covariance‐driven SSI (COV‐SSI) has been proposed in this research, referred to as the CEEMDAN‐SSI algorithm. The CEEMDAN‐SSI algorithm first decomposes the structural vibration acceleration into intrinsic mode functions (IMFs) and then selects the pertinent IMF component for signal reconstruction using the Pearson correlation coefficient. Subsequently, the reconstructed signal undergoes analysis using the COV‐SSI algorithm, effectively mitigating the occurrence of false modes. Furthermore, the research focuses on a large‐span continuous rigid frame bridge with elevated piers situated in Toutunhe, Xinjiang Province, currently under construction. Modal parameters of the rigid frame bridge under various wind speed conditions are compared and analyzed using both COV‐SSI and CEEMDAN‐SSI algorithms. The findings reveal that the CEEMDAN‐SSI algorithm markedly diminishes false modes while enhancing the strength of stability axes for each mode, thus affirming the feasibility and robustness of the CEEMDAN‐SSI algorithm.
... Recently, several researchers have introduced various time-frequency analysis techniques, including the wavelet transform (WT) (Adeli & Jiang, 2006;Cruz & Salgado, 2009;Giurgiutiu & Yu, 2003;Guo & Kareem, 2016a;Khoa, 2013;Melhem & Kim, 2003;Nagarajaiah & Basu, 2009;Qiao et al., 2012;Staszewski & Robertson, 2007;Tang et al., 2010;Wong & Chen, 2001), Fourier transform (FT), short-time Fourier transform (STFT) (El Shafie et al., 2012;Giurgiutiu & Yu, 2003;Guo & Kareem, 2016a;Melhem & Kim, 2003;Nagarajaiah & Basu, 2009), Hilbert transform (HT) (Feldman, 2014;Kunwar et al., 2013;Loutridis, 2004;Pines & Salvino, 2006;Roy et al., 2019;Salvino et al., 2003;Si et al., 2016), and the Wigner-Ville distribution (WVD) (Berinde et al., 2006;Bradford et al., 2006;G. Chen et al., 2013;Claasen & Mecklenbräuker, 1980;Guo & Kareem, 2016b;Martin & Flandrin, 1985;Tang et al., 2010;Wu & Chiang, 2009) as non-parametric strategies for system identification (Salvino et al., 2003). ...
The role of signal-based nonlinear system identification methods for the rapid post-earthquake damage assessment of reinforced concrete (RC) bridge piers is explored. Experimental data from the shaking table tests of six RC columns with and without corrosion damage are used as benchmark data. The specimens are excited under three different ground motions with different time-series characteristics, structural detailing, and corrosion levels. The proposed system identification methods make use of accelerations alone (but not displacements as these are costly in-situ) to estimate the instantaneous frequency. The Wigner-Ville distribution and Hilbert transform are utilised due to their high resolution in both time and frequency domains. A combination of modal filtering and thresholding, using instantaneous amplitudes, are employed to attenuate the unreliable spikes in the Hilbert transform's instantaneous frequency estimates. Their performance is benchmarked against a moving linear regression and standard white-noise tests. The comparison of the experimental results and time-frequency analysis indicates that the Wigner-Ville distribution and the Hilbert transform can produce reliable rapid damage detection when the response amplitude is large. The Wigner-Ville distribution has better robustness and higher resolution. The robustness of the more computationally efficient Hilbert transform can be significantly improved by the introduction of modal filtering and thresholding.
... The empirical mode decomposition (EMD) technique decomposes the signal in lower orders and illustrates its new features at each step. This method has been implemented for signal comparison purposes in damaged and undamaged structures to highlight the signal variation at different decay conditions [21]. ...
Structural health monitoring (SHM) is crucial in preserving the civil infrastructure asset and ensuring safety of the operations. Amongst the available SHM techniques, the ground-based synthetic aperture radar (GB-SAR) is one of the most reliable. However, a gap in knowledge with the use of this system exists when multiple targets are in the same acquisition range. The present study investigates into this aspect and proposes a two-stage procedure based on i) controlling the signal propagation characteristics during the data collection and ii) implementing advanced signal processing techniques to aid the interpretation of the measured signal. To this effect, three scenarios of interest are implemented in the laboratory environment, i.e., i) absence of targets, ii) presence of one target, and iii) presence of two targets in the centerline of the radar. The data collection is aided by augmented reality (AR), which allows to visualise the radar footprint and precisely control the acquisition according to the set scenarios. The collected data are processed using the empirical
mode decomposition (EMD) and the Hilbert-Huang transform (HHT) techniques. The proposed methodology is shown to be effective in both the data control and processing stages. Results have proven that the signal response from multiple targets differs from that observed in the other investigated scenarios, hence showing potential for enhancing multi-target detection in structures with GB-SAR.
... Mahalanobis distance [25] is usually used to assess the change between the reference sample and the testing sample to judge whether the structure has been damaged [26]. The specific formula is as follows: ...
Damage identification is a key issue in structural health monitoring and safety state assessment. Damage information extraction from measurements is difficult due to environmental noise and ambient excitation, which greatly reduce the accuracy of structural damage identification. In this study, a structural damage information amplification method based on Mahalanobis distance cumulant (MDC) and intrinsic mode function (IMF) was proposed. Firstly, the measurements of the structure were decomposed by the empirical mode decomposition (EMD) technology, and the relative energy change rate of each order IMF was used to screen the damage-sensitive component. By comparing the damage identification vectors constructed by MDC values from the raw measured parameters, the damage-sensitive component can obtain more damage information making damage detecting efficient. Meanwhile, the area difference of the probability density function of MDC values was used to assess the damage information amplification to determine the appropriate level of accumulation by using the cyclic analysis procedure. The model simulations and experiments were carried out to verify the method. The results showed that the selected damage-sensitive component used for constructing MDC values can amplify the damage information and make better accuracy for damage identification.
... In previous studies, sine and sweep sine waves were extensively used as excitation signals. Fast Fourier Transform (FFT) [12], Wavelet [13], Cepstrum [14], and Mode Decomposition [15] methods were used for the analysis of the monitored signals. A new excitation signal consisting of multiple pulses with different widths was introduced in this study, which eliminated the need for a signal generator and could be produced using only digital electronic circuits. ...
Fabricating complex parts using additive manufacturing is becoming more popular in diverse engineering sectors. Structural Health Monitoring (SHM) methods can be implemented to reduce inspection costs and ensure structural integrity and safety in these parts. In this study, the Surface Response to Excitation (SuRE) method was used to investigate the wave propagation characteristics and load sensing capability in conventionally and additively manufactured ABS parts. For the first set of the test specimens, one conventionally manufactured and three additively manufactured rectangular bar-shaped specimens were prepared. Moreover, four additional parts were also additively manufactured with 30% and 60% infill ratios and 1 mm and 2 mm top surface thicknesses. The external geometry of all parts was the same. Ultrasonic surface waves were generated using three different signals via a piezoelectric actuator bonded to one end of the part. At the other end of each part, a piezoelectric disk was bonded to monitor the response to excitation. It was found that hollow sections inside the 3D printed part slowed down the wave travel. The Continuous Wavelet Transform (CWT) and Short-Time Fourier Transform (STFT) were implemented for converting the recorded sensory data into time–frequency images. These image datasets were fed into a convolutional neural network for the estimation of the compressive loading when the load was applied at the center of specimens at five different levels (0 N, 50 N, 100 N, 150 N, and 200 N). The results showed that the classification accuracy was improved when the CWT scalograms were used.
... The unwrapped instantaneous Hilbert phase (UIHP) was shown to be informative about damage [26]. For instance, Pines and Salvino [27] demonstrated that the phase expression of structural vibration characteristics is sensitive to the variations in various structural parameters such as stiffness, mass, and damping. The authors proved that the Hilbert instantaneous phase is an effective damage sensitive feature. ...
In this paper, a novel method is proposed for damage detection of structures with closely-spaced eigenvalues. The proposed method uses a transformed form of the condensed frequency response function matrix each of whose columns is obtained as the sum of the unwrapped instantaneous Hilbert phase of the corresponding decomposed column of the original matrix using Empirical Mode Decomposition (EMD) algorithm. A new sensitivity-based model updating equation is then developed, which uses the constructed new matrix as input. The constructed sensitivity-based equation is solved via the least squares method through iterations to update unknown structural damage indices in a finite element model of the structure. To demonstrate the capability of the proposed method, the problem of damage detection in a composite laminate plate and a spatial truss structure, as examples of structures with closely-spaced eigenvalues, is solved. Moreover, the results obtained from the proposed method are compared against two other methods from the literature. The results show that the proposed method is far more effective at updating damage indices when incomplete highly noisy data is available.
... The ill-posedness of such problems results from a number of actualities, not limited to uncertainties in environmental conditions (wind, temperature, ground conditions, humidity, etc.), traffic, measurement noise, the discrete nature of measurements, material characteristics and numerical modelling error. One of the most pervasive frameworks used in solving dynamical inverse problems is model updating, which generally aims to match a physics-based model (such as a representative finite-element model) to measured dynamical data [73,89], commonly using a form of modal analysis [155][156][157]. The physics-based techniques are particularly efficient in providing higher accuracy when testing is restricted. ...
The field of structural engineering is vast, spanning areas from the design of new infrastructure to the assessment of existing infrastructure. From the onset, traditional entry-level university courses teach students to analyse structural responses given data including external forces, geometry, member sizes, restraint, etc.—characterizing a forward problem (structural causalities → structural response). Shortly thereafter, junior engineers are introduced to structural design where they aim to, for example, select an appropriate structural form for members based on design criteria, which is the inverse of what they previously learned. Similar inverse realizations also hold true in structural health monitoring and a number of structural engineering sub-fields (response → structural causalities). In this light, we aim to demonstrate that many structural engineering sub-fields may be fundamentally or partially viewed as inverse problems and thus benefit via the rich and established methodologies from the inverse problems community. To this end, we conclude that the future of inverse problems in structural engineering is inexorably linked to engineering education and machine learning developments.
... Frameworks used in solving dynamical inverse problems in SHM are widely reported in the literature. One of the most pervasive approaches is model updating, which generally aims to match a physics-based model (such as a representative finite element model) to measured dynamical data [88,72], commonly using a form of modal analysis [151,152]. The physics-based techniques are particularly efficient in providing higher accuracy when testing is restricted. ...
The field of structural engineering is vast, spanning areas from the design of new infrastructure to the assessment of existing infrastructure. From the onset, traditional entry-level university courses teach students to analyse structural response given data including external forces, geometry, member sizes, restraint, etc. - characterising a forward problem (structural causalities → structural response). Shortly thereafter, junior engineers are introduced to structural design where they aim to, for example, select an appropriate structural form for members based on design criteria, which is the inverse of what they previously learned. Similar inverse realisations also hold true in structural health monitoring and a number of structural engineering sub-fields (response → structural causalities). In this light, we aim to demonstrate that many structural engineering sub-fields may be fundamentally or partially viewed as inverse problems and thus benefit via the rich and established methodologies from the inverse problems community. To this end, we conclude that the future of inverse problems in structural engineering is inexorably linked to engineering education and machine learning developments.
... It is significant to mention that the main idea of the proposed IMF selection approach originates from the theory of the modal participation factor regarding the structural dynamics and modal analysis (Paultre 2011). Inspired by this theory, one can define =90% to choose sufficient and optimal IMFs automatically. ...
This book conducts effective research on data-driven Structural Health Monitoring (SHM), and accordingly presents many novel feature extraction methods by time series analysis and signal processing, to extract reliable damage sensitive features from vibration responses. In this regard, some limitations of time series modeling are dealt with. For decision-making, innovative distance-based novelty detection techniques are presented to detect, locate, and quantify different damage scenarios. The performance of the presented methods is demonstrated via laboratory and full-scale structures along with several comparative studies. The main target audience of the book includes scholars, graduate students working on SHM via statistical pattern recognition in terms of feature extraction and classification for damage diagnosis under environmental and operational variations; it would also be beneficial for practicing engineers whose work involves these topics.
... It is significant to mention that the main idea of the proposed IMF selection approach originates from the theory of the modal participation factor regarding the structural dynamics and modal analysis (Paultre 2011). Inspired by this theory, one can define =90% to choose sufficient and optimal IMFs automatically. ...
Feature extraction by signal processing algorithms is a key element of the data-driven methods. Most of the conventional signal-processing techniques in time and frequency domains are limited to analyze stationary vibration data. On this basis, the serious drawback of such approaches is an inability to analyze non-stationary signals. Due to the probability of measuring non-stationary vibration responses from ambient excitation sources, the direct use of time-domain and frequency-domain signal processing techniques may be problematic. In this chapter of the book, time-frequency signal decomposition algorithms are introduced as alternative options for feature extraction. However, the main problem is that decomposed components from these algorithms may not fully be informative for using in an SHM strategy with different uncertainties. In such a case, the components extracted from such time-frequency signal decomposition algorithms may not sufficiently sensitive to damage. To overcome this limitation, this chapter proposes a hybrid approach as a combination of an adaptive time-frequency signal decomposition algorithm and a time series model so as to extract damage-sensitive features from non-stationary signals caused by ambient vibration.
... However, this damage identification method is greatly influenced by noise and damage severity. erefore, the solution is to combine this method with the Hilbert spectrum and some more sensitive damage identification methods [28][29][30][31]. e core of the EMD method is to decompose the signal into a set of intrinsic mode functions. ...
Data-driven damage identification based on measurements of the structural health monitoring (SHM) system is a hot issue. In this study, based on the intrinsic mode functions (IMFs) decomposed by the empirical mode decomposition (EMD) method and the trend term fitting residual of measured data, a structural damage identification method based on Mahalanobis distance cumulant (MDC) was proposed. The damage feature vector is composed of the squared MDC values and is calculated by the segmentation data set. It makes the changes of monitoring points caused by damage accumulate as “amplification effect,” so as to obtain more damage information. The calculation method of the damage feature vector and the damage identification procedure were given. A mass-spring system with four mass points and four springs was used to simulate the damage cases. The results showed that the damage feature vector MDC can effectively identify the occurrence and location of the damage. The dynamic measurements of a prestress concrete continuous box-girder bridge were used for decomposing into IMFs and the trend term by the EMD method and the recursive algorithm autoregressive-moving average with the exogenous inputs (RARMX) method, which were used for fitting the trend term and to obtain the fitting residual. By using the first n-order IMFs and the fitting residual as the clusters for damage identification, the effectiveness of the method is also shown.
... The EMD algorithm has been shown to be very effective in decomposing non-stationary and nonlinear signals and, therefore, is recognised as an effective method for the purpose of this paper. EMD has been also used in other context of SHM by many researchers so far [35][36][37][38][39]. ...
A new signal reconstruction is proposed for damage detection on a simply supported beam using multiple measurements of displacement induced by a moving sprung mass. The new signal is constructed from the difference between the spatially integrated deflection for the intact (baseline) and damaged beams under quasi-static loading. To that end, it is shown that the static component of displacement from the dynamic moving mass experiment may be extracted very effectively using a robust smoothing technique and that this outperforms some comparable techniques. It is shown that by measuring displacement at a modest number of points on the beam the new reconstructed signal is able to detect the location of the damage more accurately than methods that use only a single-point data. In particular, the technique is able to detect damage present simultaneously at multiple locations and can do so with a highly variable moving mass velocity. In order to construct an a posteriori baseline, the strain data from the same traverse could be used to recover the displacement-time history of the intact beam, which could enhance the method by enabling the baseline to be determined from the same experiment, further eliminating effects of experimental conditions if required. However, a Monte Carlo simulation is run to consider the effect of signal noise, showing that the proposed damage detection strategy locates damage even in the presence of noise of 50% in the measured signals ().
... Recently, several researchers introduced time-frequency representatives including the wavelet transform (WT) (Adeli & Jiang, 2006;Cruz & Salgado, 2009;Giurgiutiu & Yu, 2003;Guo & Kareem, 2016a;Khoa, 2013;Melhem & Kim, 2003;Nagarajaiah & Basu, 2009;Qiao, Esmaeily, & Melhem, 2012;Spanos, Giaralis, Politis, & Roesset, 2007;Spanos & Failla, 2005;Staszewski & Robertson, 2007;Tang, Liu, & Song, 2010;Wong & Chen, 2001), the Fourier transform (FT), the short-time Fourier transform (STFT) (El Shafie, Noureldin, McGaughey, & Hussain, 2012;Giurgiutiu & Yu, 2003;Guo & Kareem, 2016a;Melhem & Kim, 2003;Nagarajaiah & Basu, 2009), the Hilbert transform (HT) (Feldman, 2014;Kunwar, Jha, Whelan, & Janoyan, 2013;Loutridis, 2004;Pines & Salvino, 2006;Roy et al., 2019;Salvino, Pines, Todd, & Nichols, 2003;Si, Wang, Si, & Wang, 2016) and the Wigner-Ville distribution (WVD) ( Berinde, Gillich, & Chioncel, 2006;Bradford, Yang, & Heaton, 2006;G. Chen, Chen, & Dong, 2013;Claasen & Mecklenbr€ auker, 1980;Guo & Kareem, 2016b;Martin & Flandrin, 1985;Tang et al., 2010;Wu & Chiang, 2009 ) as non-parametric system identification strategies (Salvino et al., 2003). ...
The role of signal-based nonlinear system identification methods for the rapid post-earthquake damage assessment of reinforced concrete (RC) bridge piers is explored. Experimental data from the shaking table tests of six RC columns with and without corrosion damage are used as benchmark data. The specimens are excited under three different ground motions with different time-series characteristics, structural detailing, and corrosion levels. The proposed system identification methods make use of accelerations alone (but not displacements as these are costly in-situ) to estimate the instantaneous frequency. The Wigner-Ville distribution and Hilbert transform are utilised due to their high resolution in both time and frequency domains.
A combination of modal filtering and thresholding, using instantaneous amplitudes, are employed to attenuate the unreliable spikes in the Hilbert transform’s instantaneous frequency estimates. Their performance is benchmarked against a moving linear regression and standard white-noise tests. The comparison of the experimental results and time-frequency analysis indicates that the Wigner-Ville distribution and the Hilbert transform can produce reliable rapid damage detection when the response amplitude is large. The Wigner-Ville distribution has better robustness and higher resolution. The robustness of the more computationally efficient Hilbert transform can be significantly improved by the introduction of modal filtering and thresholding.
... In terms of signal processing algorithms, the Hilbert-Huang transform (HHT) has been widely used in the context of structural health monitoring [27,28] since the empirical mode decomposition (EMD) algorithm was first introduced by Huang et al. [29]. In fact the EMD algorithm has been employed as an effective method for fault diagnosis in a variety of other scientific fields [30,31]. ...
Holes and knots are common defects that occur in wood that affect its value for both structural and high-end aesthetic applications. When these defects are internal to wood they are rarely evident from visual inspection. It is therefore important to develop techniques to detect and analyse these defects both in standing trees prior to harvesting them and in processed timber and/or completed wooden structures. This paper presents an effective method to detect and analyse hole defects in wood. The method uses the recorded output wave signal from an ultrasonic device tested on rectangular wood samples. The ultrasonic wave signal is decomposed into its constructive modes using Empirical Mode Decomposition (EMD). This process decomposes a non-stationary non-linear wave signal into its semi-orthogonal bases known as intrinsic mode functions (IMFs). A matrix of all IMFs (except the residual IMF) is then assembled and its covariance matrix derived. The research demonstrates through several experimental studies that the maximum eigenvalue of the proposed covariance matrix is more sensitive to hole defects in wood than traditionally used measures such as time-of-flight. The results provide evidence that the proposed damage sensitive feature (DSF) can successfully detect hole defects in hardwood samples but further work is recommended on its application to other materials. It is anticipated that this method will have wide applicability in the forestry and timber industries for aiding in product value determination.
... Many attempts have been made to monitor faults or the health condition of a dynamic system by using deviations in the vibration characteristics. In order to diagnose the health condition of a machine, researchers have used signal processing techniques to analyze the vibration response, such as fast Fourier transform [18][19][20][21], envelope [22][23][24], cepstrum [25][26][27][28][29] and wavelet [30][31][32][33] analysis. The processed signals provided information on the spectral response of a machine. ...
With the rapid progress in the deep learning technology, it is being used for vibration-based structural health monitoring. When the vibration is used for extracting features for system diagnosis, it is important to correlate the measured signal to the current status of the structure. The measured vibration responses show large deviation in spectral and transient characteristics for systems to be monitored. Consequently, the diagnosis using vibration requires complete understanding of the extracted features to discard the influence of surrounding environments or unnecessary variations. The deep-learning-based algorithms are expected to find increasing application in these complex problems due to their flexibility and robustness. This review provides a summary of studies applying machine learning algorithms for fault monitoring. The vibration factors were used to categorize the studies. A brief interpretation of deep neural networks is provided to guide further applications in the structural vibration analysis.
... In this sense, the analogy with structural vibrations is straightforward. Some other examples of contamination between the speech processing techniques and structural health monitoring include some recent works on Wavelet Levels (WLs), on Hilbert-Huang Transform (HHT), and on Empirical Mode Decomposition (EMD) [13,14]. Other proposals include well-known techniques, such as the Continuous Wavelet Transform (CWT), the Unscented Kalman Filter (UKF), and the Blind Source Separation (BSS) [5]. ...
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This paper presents a damage sensitive feature, the Teager-Kaiser Energy Cepstral Coefficients (TECCs), which can be used to train a Machine Learning algorithm to perform damage detection and Structural Health Monitoring (SHM) on complex buildings and/or mechanical systems.
Abstract
Recently, features and techniques from speech processing have started to gain increasing attention in the Structural Health Monitoring (SHM) community, in the context of vibration analysis. In particular, the Cepstral Coefficients (CCs) proved to be apt in discerning the response of a damaged structure with respect to a given undamaged baseline. Previous works relied on the Mel-Frequency Cepstral Coefficients (MFCCs). This approach, while efficient and still very common in applications, such as speech and speaker recognition, has been followed by other more advanced and competitive techniques for the same aims. The Teager-Kaiser Energy Cepstral Coefficients (TECCs) is one of these alternatives. These features are very closely related to MFCCs, but provide interesting and useful additional values, such as e.g., improved robustness with respect to noise. The goal of this paper is to introduce the use of TECCs for damage detection purposes, by highlighting their competitiveness with closely related features. Promising results from both numerical and experimental data were obtained.
... Applying physics-based models, the location and severity of damage were determined by tracking phase properties between consecutive degrees of freedom. They verified the proposed technique experimentally (Pines & Salvino, 2006). Some techniques are developed using optimization methods along with HHT. ...
Extensive research has been carried out on vibration-based structural health monitoring in the last few decades. A large number of these studies focus on response-based techniques due to its ease and efficiency. The main concern in such investigations is to extract a proper damage indicative feature from response data. This paper presents a new scheme in decomposing response data in order to extract a structural damage feature. Individual points on the structure body have their own time response signal. All these signals decomposed simultaneously through Multi-channel Empirical Mode Decomposition. Decomposed data of all structural points are put together to form a virtual structural deflection shape over time for each decomposed base vector. These time dependent deflection shapes are employed as a feature to determine damage location, if any. The proposed method was implemented both numerically and experimentally. In all cases, the proposed technique was able to locate the damaged zone successfully.
... Therefore, EMD is highly adaptable and can extract the non-stationary components from the given signals. EMD has been extensively used for damage detection in SHM [13][14][15]. To solve the mode mixing problem in EMD, the ensemble EMD (EEMD) was further developed by Wu and Huang [16]. ...
This paper proposes a methodology to process and interpret the complex signals acquired from the health monitoring of civil structures via scale-space empirical wavelet transform (EWT). The FREEVIB method, a widely used instantaneous modal parameters identification method, determines the structural characteristics from the individual components separated by EWT first. The scale-space EWT turns the detecting of the frequency boundaries into the scale-space representation of the Fourier spectrum. As well, to find meaningful modes becomes a clustering problem on the length of minima scale-space curves. The Otsu’s algorithm is employed to determine the threshold for the clustering analysis. To retain the time-varying features, the EWT-extracted mono-components are analyzed by the FREEVIB method to obtain the instantaneous modal parameters and the linearity characteristics of the structures. Both simulated and real SHM signals from civil structures are used to validate the effectiveness of the present method. The results demonstrate that the proposed methodology is capable of separating the signal components, even those closely spaced ones in frequency domain, with high accuracy, and extracting the structural features reliably.
... EMD is comparatively a far better technique than the other time and frequency domain techniques and finds application in numerous fields, such as nuclear physics [15], image processing [16], biomedical diagnostics [17], ocean and seismic engineering [18,19] and structural testing [20]. EMD is used for mechanical and rotary machinery faults diagnosis such as beam crack detection [21], structural health monitoring [22], rolling bearings fault diagnosis [23÷25], gear fault diagnosis [19, 26÷27, 28], rub signal analysis and rotor startup signal processing [29]. ...
Rotating machinery holds a noteworthy role in industrial applications and covers a wide range of mechanical equipment. Vibration analysis using signal processing techniques is generally utilized for condition monitoring of rotary machinery and engineering structures in order to prevent failure, reduce maintenance cost and to enhance the reliability of the system. Empirical mode decomposition (EMD) is amongst the most substantial non-linear and non-stationary signal processing techniques, and it has been widely utilized for fault detection in rotary machinery. This paper presents the EMD, time waveform and power spectrum density (PSD) analysis for localized spur gear fault detection. Initially, the test model was developed for vibration analysis of single tooth breakage of spur gear at different RPMs and then specific fault was introduced in driven gear under different damage conditions. The recorded data, by wireless tri-axial accelerometer, was then analyzed using EMD and PSD techniques and results have been plotted. Results depicted that EMD algorithms are found to be more functional than the ordinarily used PSD and time waveform techniques.
... In this sense, the analogy with structural vibrations is straightforward. Some other examples of contamination between the speech processing techniques and structural health monitoring include some recent works on Wavelet Levels (WLs), on Hilbert-Huang Transform (HHT), and on Empirical Mode Decomposition (EMD) [13,14]. Other proposals include well-known techniques, such as the Continuous Wavelet Transform (CWT), the Unscented Kalman Filter (UKF), and the Blind Source Separation (BSS) [5]. ...
... It was found [10][11][12] that the obtained results ( 13 CO 2 measuring accuracy and the boundary 13 CO 2 / 12 CO 2 ratio by simultaneous measurement of the 13 CO 2 and 12 CO 2 content in the expiratory air) may be substantially improved by using different experimental signal filtering algorithms-an empirical mode decomposition algorithm (EMD) [13][14][15][16][17][18], Kalman filter [19], and Wiener filter [19,20]. ...
... To reduce the effect of noise, a number of methods are used, among which one of the most promising is the use of various adaptive filtering algorithms for an experimental signal. The empirical mode decomposition algorithm (EMD) [10][11][12][13][14][15][16], Kalman filters [17,18], and Wiener filters [18][19][20][21][22] are the most common of these filters. They have often been used over recent years in gas analysis problems as effective tools for increasing the signal-to-noise ratio. ...
... However, the phase information of fNIRS signals that have very important physical significance, might also serve as a neural indicator for various cognition process and brain disorders. Importantly, the phase data [24,25] of fNIRS signals can be generated via the Hilbert transform [26][27][28], which can be further utilized to identify the brain activation regions and to construct the brain networks. In this study, it is hypothesized the brain activation/networks generated from https://doi.org/10.1016/j.bbr.2018.12.032 ...
In this study, a phase method for analyzing functional near-infrared spectroscopy (fNIRS) signals was developed, which can extract the phase information of fNIRS data by using Hilbert transform. More importantly, the phase analysis method can be further performed to generate the brain phase activation and to construct the brain networks. Meanwhile, the study of translation between Chinese and English has been exciting and interesting from both the language and neuroscience standpoints due to their drastically different linguistic features. In particular, inspecting the brain phase activation and functional connectivity based on the phase data and phase analysis method will enable us to better understand the neural mechanism associated with Chinese/English translation. Our phase analysis results showed that the left prefrontal cortex, including the dorsolateral prefrontal cortex (DLPFC) and frontopolar area, was involved in the translation process of the language pair. In addition, we also discovered that the most significant brain phase activation difference between translating into non-native (English) vs. native (Chinese) language was identified in the Broca’s area. As a result, the proposed phase analysis approach can provide us an additional tool to reveal the complex cognitive mechanism associated with Chinese/English sight translation.
In structural health monitoring (SHM), the integration of a model-free approach with blind source separation (BSS) offers a potent combination for damage detection. A model-free approach, devoid of reliance on predefined structural models, provides flexibility and adaptability, especially when dealing with complex structures or those with evolving characteristics. In addition, BSS is particularly suited for isolating individual sources from mixed signals, even in noisy environments. In this context, this research presents ADACTA (ADvAnced ComponenT Analysis), a method for SHM that combines the capabilities of principal component analysis (PCA) and independent component analysis (ICA). First, PCA is employed for data normalization and dimensionality reduction; then, ICA emphasizes damage-induced vibration signatures. Together, PCA and ICA offer a robust combination to extract reliable damage-sensitive features: PCA streamlines data, while ICA ensures that separated signals best represent underlying structural changes, as mathematically proved in the present work. Appropriate metrics (i.e., city block distance and Pearson correlation coefficient) are introduced to quantify the distance between signals acquired in different time intervals, serving as damage indicators. The technique can be applied for detecting early-stage damages, allowing the examination of the temporal evolution of the introduced damage indicators. The ADACTA method was tested on the Z24 bridge database, demonstrating its potential for improved early-stage damage detection in real-world structures.
One of the serious issues of traditional signal processing techniques in analyzing the responses of real-life structures is related to the presentation of fundamental information of nonlinear, non-stationary, and noisy signals with closely-spaced frequencies. To overcome this difficulty, numerous studies have been carried out recently to explore proper time-frequency signal processing techniques to efficiently present high-resolution representations for nonlinear characteristics of analyzed signals. Despite existing extensive reviews on vibration-based signal processing techniques in time and frequency domains for Structural Health Monitoring purposes, there exists no study in categorizing the signal processing techniques based on the feature extraction with time-frequency representations. To fill this gap, this paper presents a comprehensive state-of-the-art review on the applications of time-frequency signal processing techniques for damage detection, localization, and quantification in various structural systems. The progressive trend of time-frequency analysis methods is reviewed by summarizing their advantages and disadvantages, as well as recommendations of combination methods to be utilized for different applications in various complicated structural and mechanical systems.
Accurate modeling of guided wave propagation is crucial for structural health monitoring (SHM) systems, where a large amount of information and cases are needed to cover all in-service conditions of a structure. Finite-element models have proven to be accurate enough to simulate the problem; however, they typically require substantial computational resources, and each simulation may require a significant amount of time. This article presents a comprehensive study of a ray-tracing-based wave propagation methodology applied to predict the acoustic behavior of lightweight structures. Focused on composite materials, particularly carbon fiber-reinforced plastic (CFRP), the study addresses the growing need for accurate and fast simulation tools in industries where high-strength lightweight materials play a pivotal role, such as aerospace or automotive. The study presents an examination of the ray tracing method’s effectiveness with series of experimental coupon tests, ranging from a simple metallic plate to a representative CFRP wing lower cover of the Universidad Politécnica de Madrid-LIBIS Unmanned Aerial Vehicle. The investigation spans a distribution of possible damage locations ensuring a comprehensive applicability evaluation. Results demonstrate efficacy in predicting the wave propagation characteristics, including transmission, reflection, and absorption within composite structures, and also an accurate representation of its behavior for in-service damages, both via added masses and real impact damages. The validation involves an in-detail comparison with experimental measurements, evaluating the reliability and applicability of the ray tracing approach. This research not only contributes to the advancement of predictive modeling for acoustic behavior in composite structures but also addresses the broader implications for industries relying on accurate simulations for design optimization and performance evaluation. The validated ray tracing method has proven to be a valuable tool to ensure precise predictions of wave propagation in composite materials, and its computation speed makes the methodology ideal to contribute to a training database for a possible physics-informed machine learning SHM system.
This study has been investigated using the new criterion measuring complexity Hilbert-Huang entropy (HHE), changes, and fluctuations in groundwater levels under the influence of climate change factors and humans. In this regard, the 120-month time series of groundwater level, precipitation, temperature, and runoff parameters (period 2009–2018) are first divided into five 24-month periods, then by applying the Hilbert-Huang transform. Eachperiod is decomposed down into smaller periods, and finally, the HHE criterion measures the complexity of the time series. The examination of changes in the HHE complexity criterion shows a decrease of 2.02, 2.93, and 29.58% in the groundwater level in the second, third, and fourth periods. Also, according to the results of changes in the complexity of precipitation and temperature time series as climate change factors, these two parameters have decreased in the third and fourth periods, with the rate of decrease for the temperature time series being 18.8 and 8.3%, respectively, and for the precipitation time series is obtained by 30.6 and 4.4%, respectively. Hence, according to the results, the discharge parameter, as a human factor in the second and fourth periods, shows a decrease of 8.6 and 39.1%, respectively.
The vibration signal is an effective diagnostic tool in structural health monitoring (SHM) fields that is closely related to abnormal states. Deep learning methods have got remarkable success in utilizing vibration signals for damage detection. This paper presents a systematic review of deep learning methods for SHM, focusing on the utilization of vibration signal data from different model perspectives. In recent years, there has been a significant increase in research on deep learning for vibration-based SHM. The accuracy of such works is equivalent to that of traditional machine learning approaches, and better results could be achieved by integrating multiple approaches. Furthermore, we found that transfer learning methods yield promising results when limited data are available to train the model. This paper aims to comprehensively review deep learning research on health monitoring using vibration signal data from multiple perspectives, with a particular emphasis on transfer learning methods for SHM. It fills the gap that existing reviews lack in the discussion of transfer learning for SHM. Finally, we analyze the challenges faced by current research and provide recommendations for future work.
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Context: In recent years, thanks to technological advances in instrumentation and digital signal processing, noninvasive methods to detect structural damage have become increasingly important. Vibration-based structural health monitoring (SHM) techniques allow detecting the presence and location of damage from permanent changes in the fundamental frequencies of signals. A successfully employed method for damage detection is empirical mode decomposition (EMD). Another method, less used in this field of study, is singular spectral analysis (SSA). This paper describes both methods and presents a simulation study aimed at comparing them and identifying which one is more effective in detecting structural damage. Method: The methods of a reference study known as benchmark SHM were applied to facilitate the comparison. To evaluate the effectiveness of both methods, Monte Carlo simulation was employed. To control the random noise and other factors inherent to the simulation, the procedure was repeated 1.000 times for each type of damage. Results: In the case of severe damage, both methods showed a good performance. However, when the damage was slight, the changes in the fundamental frequency were not apparent. However, a significant change in the amplitude level was observed. In this case, SSA obtained the best results.
Identifying and tracking transient fluid responses has long been challenging due to the inherent and correlated complexities in both spatial and temporal domains. Kernel mode decomposition (KMD) is a newly proposed method capable of capturing the transitioning amplitude and frequency locally. In this study we extend the KMD with a sparsification network that groups the response modes based on their spectral and spatial proximity using an energylike index to instigate systems with transitional behaviors. A synthetic problem setup is used to demonstrate how the proposed method can identify essential modes with changing both amplitude and frequencies. A two-sided oscillating lid-driven cavity flow problem demonstrates that the KMD network can further track the transition of modes even when spatial distributions vary over time. Finally, we inspect the formation process of a laminar separation bubble with the proposed method and isolate multiple competing mechanisms involved in the process. These results reveal that KMD can extend the application of modal analysis methods to identify transitioning spatial structures associated with varying frequency in an interpretable fashion, a necessary step for their use for understanding broad dynamic systems.
In online structural health monitoring of the fixed offshore jacket platform, the determination of the time‐dependent degradation of structures due to damages is the most important step in a maintenance strategy. This paper presents the application of the Hilbert Huang transform method based on the iEEMD (improved ensemble empirical mode decomposition) algorithm to identify the instantaneous natural frequency degradation due to damages of the fixed offshore structure under the random wave excitation. The iEEMD algorithm is proposed to restrain the mode mixing and used to adaptively process the big response data of the offshore structure during the wave loading with a wide frequency range. The vibration response measurement experiment for the offshore structure was conducted in a wave tank in this study. The identified fundamental natural frequencies by the iEEMD‐based Hilbert Huang method were evaluated and compared with results of the numerical model of the eigenvalue analysis. The main result demonstrates that the instantaneous frequency degradation and nonlinear time‐varying behavior due to the brace damage of the fixed offshore jacket platform can be successfully identified by the iEEMD‐based Hilbert Huang transform technique under a wave load.
Additive manufacturing has been used for the production of high-value complex parts. Implementation of structural health monitoring (SHM) methods to these parts would let them gain continuous sensing and damage identification capability. The small size and very strong vibration damping characteristics of additively manufactured polymer parts do not allow the direct use of many SHM methods. In this study, detection and location estimation of compressive force applied to an additively manufactured part made of PLA was examined. The test specimen was designed with multiple skin thicknesses in each of the five zones and completely digital excitation was implemented on the part. Surface Response to the Excitation (SuRE) method was used in this study. Two piezoelectric elements were used for exciting the specimen with lamb waves from one side and recording the dynamic response to excitation at the other end of the part. The digital excitation included multiple pulses with different widths covering a wide range of exciting frequencies. Two different methods were used for damage localization, Deep Learning (DL) and the two-dimensional sum of the squares of differences (2DSSD). Short-time Fourier Transformation (STFT) was used to convert the experimental time-domain sensory data into the time–frequency domain (spectrograms). Two-dimensional images of the spectrograms were classified using 2DSSD and Convolutional Neural Network (CNN). CNN could estimate the compressive force application zone with better than 97% accuracy.
In this study, a diagnosis method was successfully implemented to identify different sounds coming from individual mechanical parts within a group of engine moving parts controlled through a variable valve timing system. The novelty of this diagnosis method is in the determination of specific sounds coming from each part within this group when they are in good working condition and without any defects. This will facilitate in early detection of faults occurring on the parts, identified through changes in the sound wave energy. Through this study, this diagnosis method was validated in three ways, namely the consistency of the results with previous studies, the synchronization of sounds from mechanical parts in overlapping cases, and the cross-correlation of engine sound modes that results from analysis using the Hilbert Huang Transform. In this paper, the distribution of sound energy according to its frequencies was utilized to distinguish which of the engine combustion chambers of a Dodge Journey 2.4 was faulty. To conduct that, the noise-based test technique was selected to record the engine sound. The results show that there is a link between the RMS energy of the engine sound and the engine output torque.
To reveal the failure mechanism of resonance effect on long-periodic structures, the spectrum characterization of nonlinear and non-stationary long-periodic ground movements are studied. Firstly, the period and energy characterizations about IMFs (intrinsic mode functions) of ground movements are analyzed. Then, an energy-weighted average period is proposed to indicate the long-periodic characterization on different types of ground movements. Lastly, the simplified method on the low-frequency time history for long-periodic ground movements is proposed and verified. The research conclusions show that, various Hilbert amplitude spectra analysis can expose all the inherent information of nonlinear and non-stationary long-periodic ground movement accurately and comprehensively. The proposed periodic parameter that characterizes different earthquake classifications can help to efficiently and conveniently filter out long-period ground movements, and it also can be used as a quantitative indicator to identify long-period ground movements. The suggested simplified method can facilitate in-depth and accurate analysis of the low-frequency components of long-periodic ground movements. Effective and accurate evaluation on the low-frequency components of long-periodic ground movements plays the key role to uncover the nonlinear dynamic behavior of long-periodic structures, and it is of great scientific research significance in the field of earthquake engineering and structural engineering.
This study aims to investigate the performance of a new damage detection method proposed based on the combination of two signal processing techniques which are complete ensemble empirical mode decomposition with adaptive noise and multiple signal classification (CEEMDAN-MUSIC). The proposed damage detection approach begins with determining the power density spectrum, namely, the pseudospectrum, from the acceleration response of a structure. Then, the CEEMDAN algorithm is used to decompose the vibration signal into a set of intrinsic mode functions (IMFs). Furthermore, the MUSIC algorithm is applied to the first IMF of the processed signal to determine the frequency pseudospectrum, prior to and post the damage states of the structure. The effectiveness of the proposed methodology is experimentally validated using a laboratory-scale model of a steel truss bridge exposed to a white noise excitation. The damage states of the truss bridge are implemented by replacing a specified diagonal element with reduced cross-sectional stiffness. The experimental results demonstrate the superiority of the CEEMDAN-MUSIC method in comparison with the performance of pure MUSIC and traditional frequency domain techniques. The advantages of the proposed technique are also discussed in terms of identifying the presence of the damage, addressing its location, and quantifying the damage levels which are summarized as the damage detection and characterization.
Los métodos no invasivos para la detección de daños estructurales han ganado cada vez mayor importancia en los últimos años debido a los avances tecnológicos de instrumentación y procesamiento digital de señales. Las técnicas de monitoreo de salud estructural basadas en vibraciones permiten identificar la presencia y ubicación del daño a partir de cambios permanentes en las frecuencias fundamentales de las señales ya que estas están directamente relacionadas con la masa y rigidez de la estructura. Un método que se ha implementado con éxito enfocado a la detección de daño es la descomposición modal empírica (EMD) y otro método poco explorado en este campo de estudio, es el análisis singular espectral (SSA).
En este trabajo se describen en detalle ambas metodologías y se realiza un estudio de simulación con el objetivo de compararlas e identificar cual es más eficaz en la detección de daño estructural. Cabe mencionar que para facilitar la comparación entre los métodos, estos se aplicaron sobre un estudio de referencia conocido como benchmark SHM problem basado en datos de respuesta estructural simulados, desarrollado por el grupo de investigación IASC-ASCE (Asociación Internacional para Control Estructural y la Sociedad Americana de Ingeniería Civil) en monitoreo de la salud estructural, el cual permite analizar distintos patrones de daño. En términos generales el SSA es más eficaz en la detección de daño dado que no es necesario filtrar la señal original para poder detectar el daño.
The accurate localization of low-velocity impacts on the composite plate structure of the ship is still a great challenge. Current research mainly focuses on extracting single domain features from impact signals as the input of machine learning methods, whereas ignores multi-domain features with more comprehensive impact information. In this paper, a hybrid support vector regression with multi-domain features is proposed to increase the localization accuracy in determining the locations of low-velocity impacts on the composite plate structure. The proposed method consists of the signal preprocessing, the multi-domain feature extraction, and the impact localization. In the signal preprocessing, the trend component in the low-velocity impact signals is eliminated by adopting the empirical mode decomposition (EMD) method. Then, the multi-domain features, which include time domain features, frequency domain features, and time-frequency domain features, are extracted from the preprocessed impact signals. Finally, the optimized support vector regression based on the bat algorithm (BA-SVR) is designed to implement the localization of low-velocity impacts. The low-velocity impact localization system using four fiber Bragg grating (FBG) sensors is established on a carbon fiber reinforced plastic (CFRP) plate, and then five sets of experiments are executed. The statistical results in these experiments demonstrate the effectiveness and feasibility of BA-SVR that uses multi-domain features and four FBG sensors and the satisfactory localization performance of the proposed method in handling the low-velocity impact localization problem on the CFRP plate.
Identifying transient modes is an important topic in multiple disciplines, but the robustness and physical interpretation of the techniques used to achieve this goal have long been challenging issues. Kernel mode decomposition (KMD) is a newly proposed method that is capable of capturing the transition of modes in both amplitude and frequency. In this study, we formulate the technique for the flow problems and employ it to understand the formation of a laminar separation bubble. Results show that KMD can capture the temporal transition between different phases of the separation bubble formation process, and can be used to extend the application of modal analysis methods to identify the spatial structures associated with each phase. The results are beneficial to improving the stability and efficiency of airfoils.
An out-put only modal parameter identification method based on variational mode decomposition (VMD) is developed for civil structure identifications. The recently developed VMD technique is utilized to decompose the free decay response (FDR) of a structure into to modal responses. A novel procedure is developed to calculate the instantaneous modal frequencies and instantaneous modal damping ratios. The proposed identification method can straightforwardly extract the mode shape vectors using the modal responses extracted from the FDRs at all available sensors on the structure. A series of numerical and experimental case studies are conducted to demonstrate the efficiency and highlight the superiority of the proposed method in modal parameter identification using both free vibration and ambient vibration data. The results of the present method are compared with those of the empirical mode decomposition-based method, and the superiorities of the present method are verified. The proposed method is proved to be efficient and accurate in modal parameter identification for both linear and nonlinear civil structures, including structures with closely spaced modes, sudden modal parameter variation, and amplitude-dependent modal parameters, etc.
This paper explores the advantages of Variational Mode Decomposition (VMD) in detecting local damage on beam type structures (bridge) subjected to a sprung mass (vehicle). VMD is used to decompose the acceleration time history of the bridge at its midspan into its constitutive intrinsic mode functions (IMFs). The instantaneous frequency (IF) and instantaneous amplitude (IA) of the first IMF show irregularities at the damage position. We demonstrate through computer simulation that VMD is superior for detecting damage when compared to the well-known Empirical Mode Decomposition (EMD) method. A new damage sensitive feature (DSF) is also introduced that considers synchronisation of peaks between the IA and IF signals. The results show that the new DSF can enhance the peak at the damage positions while suppressing peaks at other locations.
Structural health monitoring (SHM) is one of the most emerging approaches for early damage detection, which leads to improved safety and efficient maintenance of large-scale civil structures. Data-driven vibration-based SHM techniques rely on sophisticated signal processing methods to analyze and interpret the complex measured data collected from the instrumented structures. Empirical mode decomposition (EMD) is one of the robust time-frequency decomposition techniques that has been widely used in SHM. Numerous studies have used EMD and its variants in different applications specific to structural modal identification and damage detection, which have been presented in various academic journals, conference papers, and technical reports. This paper presents a comprehensive and systematic review and summary of applications of EMD and its variants that have been extensively implemented in SHM. A brief background and illustration of EMD and its variants are presented first to show their performance under various cases, followed by a detailed literature review of their recent applications specific to SHM.
Missing data, especially a block of missing data, inevitably occur in structural health monitoring systems. Because of their severe negative effects, many methods that use measured data to infer missing data have been proposed in previous research to solve the problem. However, capturing complex correlations from raw measured signal data remains a challenge. In this study, empirical mode decomposition is combined with a long short-term memory deep learning network for the recovery of the measured signal data. The proposed hybrid method converts the missing data imputation task as a time series prediction task, which is then solved by a “divide and conquer” strategy. The core concept of this strategy is the prediction of the subsequences of the raw measured signal data, which are decomposed by empirical mode decomposition rather than directly predicted, as the decomposition can assist in the modeling of the irregular periodic changes of the measured signal data. In addition, the long short-term memory network in the hybrid model can remember more long-range correlations of subsequences than can the traditional artificial neural network. Three widely used prediction models, namely, the autoregressive integrated moving average, support vector regression, and artificial neural network models, are also implemented as benchmark models. Raw acceleration data collected from a cable-stayed bridge are used to evaluate the performance of the proposed method for missing measured signal data imputation. The recovery results of the measured signal data demonstrate that the proposed hybrid method exhibits excellent performance from two perspectives. First, the decomposition by empirical mode decomposition can improve the accuracy of the core long short-term memory prediction model. Second, the long short-term memory model outperforms other benchmark models because it can fit more microscopic changes of measured values. The experiments conducted in this study also suggest that the change patterns of raw measured signal data are complex, and it is therefore important to extract the features before modeling.
Complete interfacial performances of sisal fiber (a typical plant fiber) reinforced composites (SFRCs) during the single fiber pull-out experiments were investigated experimentally with numerical simulation in the present study. The single SFRCs were found to present three-interface failure. The failure behaviors of the three interfaces were characterized by in-situ acoustic emission technique and identified as interfacial failure between technical fiber and matrix, that between elementary fibers and that between micro-fibrils of cell walls using microscope observation. Statistical analysis was employed to evaluate pull-out probability of technical fiber, elementary fibers and micro-fibrils. The embedded fiber length was concluded to dominate the failure modes of SFRCs. To further gain insight in the complete failure processes and mechanisms of the multi-layer SFRCs, a triple-interface finite element model was developed based on the cohesive zone law. Quantitative comparisons of applied stress between numerical predictions and experimental results surmised that the triple-interface model could accurately describe the multi-stage pull-out behaviors of the single SFRCs.
This paper provides an overview of methods to detect, locate, and characterize damage in structural and mechanical systems by examining changes in measured vibration response. Research in vibration-based damage identification has been rapidly expanding over the last few years. The basic idea behind this technology is that modal parameters (notably frequencies, mode shapes, and modal damping) are functions of the physical properties of the structure (mass, damping, and stiffness). Therefore, changes in the physical properties will cause detectable changes in the modal properties. The motivation for the development of this technology is presented. The methods are categorized according to various criteria such as the level of damage detection provided, model-based vs. non-model-based methods and linear vs. nonlinear methods. The methods are also described in general terms including difficulties associated with their implementation and their fidelity. Past, current and future-planned applications of this technology to actual engineering systems are summarized. The paper concludes with a discussion of critical issues for future research in the area of vibration-based damage identification.
Recently, adaptive approximation techniques have become popular for obtaining parsimonious representations of large classes of signals. These methods include method of frames, matching pursuit, and, most recently, basis pursuit. In this work, high resolution pursuit (HRP) is developed as an alternative to existing function approximation techniques. Existing techniques do not always efficiently yield representations which are sparse and physically interpretable. HRP is an enhanced version of the matching pursuit algorithm and overcomes the shortcomings of the traditional matching pursuit algorithm by emphasizing local fit over global fit at each stage. Further, the HRP algorithm has the same order of complexity as matching pursuit. In this paper, the HRP algorithm is developed and demonstrated on 1D functions. Convergence properties of HRP are also examined. HRP is also suitable for extracting features which may then be used in recognition.
A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the `empirical mode decomposition' method with which any complicated data set can be decomposed into a finite and often small number of 'intrinsic mode functions' that admit well-behaved Hilbert transforms. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and non-stationary processes. With the Hilbert transform, the 'instrinic mode functions' yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert spectrum. In this method, the main conceptual innovations are the introduction of `intrinsic mode functions' based on local properties of the signal, which make the instantaneous frequency meaningful; and th
The authors introduce an algorithm, called matching pursuit, that
decomposes any signal into a linear expansion of waveforms that are
selected from a redundant dictionary of functions. These waveforms are
chosen in order to best match the signal structures. Matching pursuits
are general procedures to compute adaptive signal representations. With
a dictionary of Gabor functions a matching pursuit defines an adaptive
time-frequency transform. They derive a signal energy distribution in
the time-frequency plane, which does not include interference terms,
unlike Wigner and Cohen class distributions. A matching pursuit isolates
the signal structures that are coherent with respect to a given
dictionary. An application to pattern extraction from noisy signals is
described. They compare a matching pursuit decomposition with a signal
expansion over an optimized wavepacket orthonormal basis, selected with
the algorithm of Coifman and Wickerhauser see (IEEE Trans. Informat.
Theory, vol. 38, Mar. 1992)
Multiresolution representations are effective for analyzing the
information content of images. The properties of the operator which
approximates a signal at a given resolution were studied. It is shown
that the difference of information between the approximation of a signal
at the resolutions 2j+1 and 2j (where j is an
integer) can be extracted by decomposing this signal on a wavelet
orthonormal basis of L 2( R n), the
vector space of measurable, square-integrable n -dimensional
functions. In L 2( R ), a wavelet orthonormal
basis is a family of functions which is built by dilating and
translating a unique function ψ( x ). This decomposition
defines an orthogonal multiresolution representation called a wavelet
representation. It is computed with a pyramidal algorithm based on
convolutions with quadrature mirror filters. Wavelet representation lies
between the spatial and Fourier domains. For images, the wavelet
representation differentiates several spatial orientations. The
application of this representation to data compression in image coding,
texture discrimination and fractal analysis is discussed
The vibratory behavior of a one dimensional spring mass system can be pictured by the superposition of traveling waves propagating along the structural network. Wave dynamics generated at natural boundaries and subsequently reflected at geometric boundaries can lead to pole-zero characteristics of a conventional Reverberated Transfer Function (RTF). By applying a wave model based virtual controller at these boundaries, a Dereverberated Transfer Function (DTF) can be obtained from the RTF. Since the DTF reveals the direct path of energy transmission across a one-dimensional structure, it is potentially useful for damage detection. In this paper, symmetric and asymmetric spring mass elements are used as the elementary cells for any arbitrary one-dimensional spring mass structure. This paper illustrates how to obtain the DTF from the RTF for discrete non-uniform structural elements. A three-degree-of-freedom (DOF) analytical building model is used for simulating several damage cases. Analytical results confirm that the DTF response can be used as a method for locating and quantifying damage in structures.
Wavelets provide a new tool for the analysis of vibration records. They allow the changing spectral composition of a nonstationary signal to be measured and presented in the form of a time-frequency map. The purpose of this paper, which is Part 1 of a pair, is to introduce and review the theory of orthogonal wavelets and their application to signal analysis. It includes the theory of dilation wavelets, which have been developed over a period of about ten years, and of harmonic wavelets which have been proposed recently by the author. Part II is about presenting the results on wavelet maps and gives a selection of examples. The papers will interest those who work in the field of vibration measurement and analysis and who are in positions where it is necessary to understand and interpret vibration data.
The time-frequency and time-scale communities have recently developed a large number of overcomplete waveform dictionaries-stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for decomposition have been proposed, including the method of frames (MOF), Matching pursuit (MP), and, for special dictionaries, the best orthogonal basis (BOB). Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l(1) norm of coefficients among all such decompositions. We give examples exhibiting several advantages over MOF, MP, and BOB, including better sparsity and superresolution. BP has interesting relations to ideas in areas as diverse as ill-posed problems, in abstract harmonic analysis, total variation denoising, and multiscale edge denoising. BP in highly overcomplete dictionaries leads to large-scale optimization problems. With signals of length 8192 and a wavelet packet dictionary, one gets an equivalent linear program of size 8192 by 212,992. Such problems can be attacked successfully only because of recent advances in linear programming by interior-point methods. We obtain reasonable success with a primal-dual logarithmic barrier method and conjugate-gradient solver.
A general method for the analysis of a time series, called the Empirical Mode Decomposition (EMD) and Hilbert Spectrum method, has recently been developed by Huang et al. This method contains two parts: the first part (EMD) decomposes any given time series data into a set of simple oscillatory functions by the repeated application of a nonlinear iterative procedure; the second part defines time-dependent amplitudes (or energies) and frequencies of the simple oscillatory functions using a Hilbert transform. In this paper, the EMD and Hilbert spectrum method is used to evaluate structural response by means of acceleration data of four different configurations of a two-dimensional welded steel frame constructed from many box beams, all filled with small viscoelastic beads. The results were compared to those of conventional methods such as modal analysis. The EMD method is also being further developed to extract damping values from experimental time series. In this approach, the damping loss factor is determined at regularly spaced frequencies associated with sampling. The method is particularly important for evaluating damping for time series data taken from an underlying physical process in which damping is dependent upon both time and frequency characteristics of the system.
The focus of this work is on damage detection in transient structural response time series data recorded during an underwater shock experiment. A unique data-driven approach where damage features are extracted, evaluated, and determined based on the instantaneous phases of structural waves was applied to detect damage for a large composite structure. Measured time series data was first decomposed adaptively into a set of basis functions, known as Intrinsic Mode Functions (IMFs), using the method of Empirical Mode Decomposition. Instantaneous phases are then defined based on the IMFs, which can be used to represent nonlinear and non-stationary signals. Damage features are then formulated and tracked in order to determine the state of a structure. This approach was developed based on a previously introduced fundamental relationship connecting the instantaneous phases of a measured time series to structural mass and stiffness parameters. A simple damage index based on the instantaneous phase relationship is used to show the effectiveness of this method for structural health monitoring applications.
Multiresolulion representations are very effective for analyzing the information content of images. We study the properties of the operator which approximates a signal at a given resolution. We show that the difference of information between the approximation of a signal at the resolutions 2 j + l and 2 j can be extracted by decomposing this signal on a wavelet orthonormal basis of L2 (Rn). In L2 (R), a wavelet orthonormal basis is a family of functions (√2j Ψ (2 Jx - π))j,n,ez2+ which is built by dilating and translating a unique functiOn Ψ(x). This decomposition defines an orthogonal multiresolulion representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror lilters. For images, the wavelet representation differentia1es several spatial orientations. We study the application of this representation to data compression in image coding, texture discrimination and fractal analysis.
The vibratory response of a structure can be represented by the superposition of traveling waves propagating slung a complex structural network. Wave dynamics generated at natural boundary conditions and subsequently reflected at geometric boundary conditions can lead to pole-zero characteristics of conventional reverberated transfer functions. However, by implementing model-based wave virtual controllers at each structural element, a dereverberated transfer function can be obtained from the measured reverberated transfer function response, Because the dereverberated transfer function represents the direct path of energy transmission across a structure, it can be used to infer damage in a structure by tracking how variations in local element properties affect the propagation of incident energy through the structure. A methodology is presented for obtaining the dereverberated transfer function response for four types of structural elements, including symmetric and asymmetric discrete spring mass elements and spectral rod and beam finite elements for continuous structures. The dereverberated transfer function response is obtained by attaching virtual controllers at the terminals of each structural element. A phase damage index method is proposed based on the relative phase propagation error from element to element to quantify the type and amount of damage. Analytical results on several simulated examples confirm that the dereverberated response can be used as a method for locating and quantifying damage in structures.
Wavelet maps provide a graphical picture of the frequency composition of a vibration signal. This paper, which is Part 2 of a pair, describes their construction and properties. In the case of harmonic wavelets, there are close similarities between wavelet maps and sonograms. A range of practical examples illustrate how the wavelet method may be applied to vibration analysis and some of its advantages.
Wavelets provide a new tool for the analysis of vibration records. They allow the changing spectral composition of a nonstationary signal to be measured and presented in the form of a time-frequency map. The purpose of this paper, which is Part 1 of a pair, is to introduce and review the theory of orthogonal wavelets and their application to signal analysis. It includes the theory of dilation wavelets, which have been developed over a period of about ten years, and of harmonic wavelets which have been proposed recently by the author. Part II is about presenting the results on wavelet maps and gives a selection of examples. The papers will interest those who work in the field of vibration measurement and analysis and who are in positions where it is necessary to understand and interpret vibration data.
We present the lifting scheme, a new idea for constructing compactly supported wavelets with compactly supported duals. The lifting scheme uses a simple relationship between all multiresolution analyses with the same scaling function. It isolates the degrees of freedom remaining after fixing the biorthogonality relations. Then one has full control over these degrees of freedom to custom design the wavelet for a particular application. The lifting scheme can also speed up the fast wavelet transform. We illustrate the use of the lifting scheme in the construction of wavelets with interpolating scaling functions.
This paper uses a damage detection approach based on dereverberated transfer functions. In one-dimensional structures, conventional reverberated transfer functions are formed because of the interactions between incident and reflected waves in structures. By applying virtual controllers to eliminate wave reflections, dereverberated transfer functions can be obtained. Dereverberated transfer functions provide good representations of a structure's local dynamics. Because local dynamics are more sensitive to parameter changes, the dereverberated transfer function appears to be suitable to infer structural damage. In this study, a three-story building model is tested under seismic wave excitation. Experimental results show that this approach can be used to locate damage, determine damage type, and quantify damage extent.
This paper develops two new adaptive wavelet transforms based on
the lifting scheme. The lifting construction exploits a spatial-domain,
prediction-error interpretation of the wavelet transform and provides a
powerful framework for designing customized transforms. We use the
lifting construction to adaptively tune a wavelet transform to a desired
signal by optimizing data-based prediction error criteria. The
performances of the new transforms are compared to existing wavelet
transforms, and applications to signal denoising are investigated
Two different procedures for effecting a frequency analysis of a
time-dependent signal locally in time are studied. The first procedure
is the short-time or windowed Fourier transform; the second is the
wavelet transform, in which high-frequency components are studied with
sharper time resolution than low-frequency components. The similarities
and the differences between these two methods are discussed. For both
schemes a detailed study is made of the reconstruction method and its
stability as a function of the chosen time-frequency density. Finally,
the notion of time-frequency localization is made precise, within this
framework, by two localization theorems
The author defines a set of operators which localize in both time
and frequency. These operators are similar to but different from the
low-pass time-limiting operator, the singular functions of which are the
prolate spheroidal wave functions. The author's construction differs
from the usual approach in that she treats the time-frequency plane as
one geometric whole (phase space) rather than as two separate spaces.
For disk-shaped or ellipse-shaped domains in time-frequency plane, the
associated localization operators are remarkably simple. Their
eigenfunctions are Hermite functions, and the corresponding eigenvalues
are given by simple explicit formulas involving the incomplete gamma
functions
This paper develops new algorithms for adapted multiscale analysis and signal adaptive wavelet transforms. We construct our adaptive transforms with the lifting scheme, which decomposes the wavelet transform into prediction and update stages. We adapt the prediction stage to the signal structure and design the update stage to preserve the desirable properties of the wavelet transform. We incorporate this adaptivity into the redundant and non-redundant transforms; the resulting transforms are scale and spatially adaptive. We study applications to signal estimation; our new transforms show improved denoising performance over existing (non-adaptive) orthogonal transforms. Supported by NSF, grant nos. MIP--9457438 and MIP--9701692, ONR grant no. N00014--95--1--0849, DARPA/AFOSR grant no. F49620-97-1-0513, and Texas Instruments. 1 1 Introduction The discrete wavelet transform (DWT) provides a very efficient representation for a broad range of real-world signals. This property has...
Planetary gearbox diagnostics using adaptive vibration signal representations
- P Samuel
- D Pines
P. Samuel, D. Pines, Planetary gearbox diagnostics using adaptive vibration signal representations, in: American Helicopter Society 57th Annual Forum, Virginia Beach, Virginia, May 9–11, 2001.
Theory of communication
- Gabor
Wavelet analysis of vibration, Part, II: wavelet maps
- Newland