The Experts below are selected from a list of 419649 Experts worldwide ranked by ideXlab platform
Gangbing Song - One of the best experts on this subject based on the ideXlab platform.
-
Monitoring of multi-bolt connection Looseness using a novel vibro-acoustic method
Nonlinear Dynamics, 2020Co-Authors: Furui Wang, Gangbing SongAbstract:Bolted connections are prone to losing their preloads with the increasing service life, thus inducing engineering accidents and economic losses in industries. Therefore, it is important to detect bolt loosening, while current structural health monitoring methods mainly focus on single-bolt joints, whose applications in industries are limited. Thus, in this paper, a novel vibro-acoustic modulation (VAM) method, is developed to detect Looseness of the multi-bolt connection. Compared to traditional VAM, the proposed method uses linear swept sine waves for both low-frequency and high-frequency excitations, which avoids a priori knowledge of the structure. Moreover, the orthogonal matching pursuit method is applied to compress original modulated signals and exclude redundant features. Then, a new entropy, namely the Gnome entropy with acronym gEn , is proposed in this paper. According to simulation analysis, the gEn has better anti-noise capacity and fewer parameters than traditional entropy. Finally, after quantifying the dynamic characteristics of compressed signals to obtain feature sets through the gEn , we feed feature sets into a random forest classifier and achieve Looseness detection of the multi-bolt connection. Moreover, the proposed method in this paper has great potential to detect other structural damages and provides guidance for further investigations on the VAM method.
-
design of a new vision based method for the bolts Looseness detection in flange connections
IEEE Transactions on Industrial Electronics, 2020Co-Authors: Chenyu Wang, Siuchun Ho, Xuemin Chen, Ning Wang, Gangbing SongAbstract:As regular inspection for the bolt connection in inaccessible areas is difficult and costly, computer vision technology provides a suitable noncontact approach for real-time bolt Looseness detection as an alternative to inspection approaches. However, computer vision still suffers from various impracticalities. In this paper, a new vision-based bolt Looseness detection method is designed and implemented with the bolt images acquired by a camera at arbitrary positions around the bolts. The new method includes the perspective transformation of original images acquired, identification of bolt positioning with the convolutional neural network digit recognition, detection of bolt rotation angles using Hough transform line detection, and density-based spatial clustering of applications with noise. To demonstrate the effectiveness of the new method, an experiment with bolted connections is setup. The experimental results demonstrate that the new method can accurately detect the Looseness of the bolts in the bolted connection.
-
monitoring of multi bolt connection Looseness using entropy based active sensing and genetic algorithm based least square support vector machine
Mechanical Systems and Signal Processing, 2020Co-Authors: Furui Wang, Zheng Chen, Gangbing SongAbstract:Abstract Looseness detection of bolted connections is an essential industrial issue that can reduce the maintenance and repair costs caused by joint failures; however, current loosening detection methods mainly focus on the single-bolt connection. Even though several methods, such as the vibration-based method and electro-mechanical impedance (EMI) method, have been employed to detect multi-bolt Looseness, while they are easily affected by environmental issues. Therefore, the main contribution of this paper is to detect loosening of the multi-bolt connection through the PZT-enabled active sensing method, which has several merits including easy-to-implement, low cost, and good ability of anti-environment disturbance. Since the current indicator of the active sensing, namely the signal energy is insensitive to multiple damages, we developed a new damage index (DI) based on the multivariate multiscale fuzzy entropy (MMFE). Subsequently, the maximum relevance minimum redundancy (mRMR) was used to select significant features from the MMFE-based DI to construct the new datasets. After feeding the new datasets into the genetic algorithm-based least square support vector machine (GA-based LSSVM), we trained a classifier to detect loosening of the multi-bolt connection. Finally, repeated experiments were conducted to demonstrate the effectiveness of the proposed method, which can guide future investigations on bolt Looseness detection.
-
modeling and analysis of an impact acoustic method for bolt Looseness identification
Mechanical Systems and Signal Processing, 2019Co-Authors: Furui Wang, Gangbing SongAbstract:Abstract Bolted joints are fundamental building blocks and have been widely used to hold multiple structural components together, while their Looseness may lead to costly disasters in industries. Compared to current bolt loosening detection methods that are often hampered due to the need for highly experienced personnel or an overly complex sensor-structure interaction, a new percussion-based method using analytical modeling and numerical simulation was proposed to reduce cost and avoid contact-type sensor installation, which is a great contribution. Analytically, the bolted joint was modeled equivalently as a laminated plate by using the virtual material method and the layer-wise theory, and its percussion-induced sound pressure level (SPL) can be obtained via the acoustic radiation mode approach. The corresponding numerical simulation was developed with the focus on the acoustic-structure coupling, and the acoustic boundary conditions were satisfied through a perfectly matched layer (PML). Compared to prior work, another contribution of this paper is that the proposed method further considers the critical effect of bolted interfacial roughness, which affects radiation sound signals significantly. Finally, acoustic tests were carried out, and the good agreement between results of modeling, simulation, and experiments demonstrate the effectiveness of the proposed method. As a rapid and non-invasive bolt Looseness detection method, the investigations in this paper can provide guidance for the future development of bolt Looseness detection methods.
-
percussion based bolt Looseness monitoring using intrinsic multiscale entropy analysis and bp neural network
Smart Materials and Structures, 2019Co-Authors: Rui Yuan, Qingzhao Kong, Gangbing SongAbstract:In this paper, a novel percussion-based bolt Looseness monitoring approach using intrinsic multiscale entropy analysis and back propagation (BP) neural network is proposed. The percussion-caused audio signals of bolt connection are decomposed by complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) to obtain intrinsic mode functions (IMFs). The IMFs are in order of the high-to-low instantaneous frequencies and contain underlying dynamical characteristic information of audio signals. The multiscale sample entropy (MSE) is improved by smoothed coarse graining process, and the proposed improved multiscale sample entropy (IMSE) values of certain IMFs can be adopted as indicators of different bolt Looseness conditions. The intrinsic multiscale entropy analysis consisting of CEEDMAN and IMSE can properly extract underlying dynamical characteristic information during audio signal processing in bolt Looseness condition identification. The obtained indicators, which are IMSE values at smallest scale factors, were employed as input in BP neural network for training and testing, to achieve accurate and stable bolt Looseness condition monitoring. The effectiveness and superiority of the proposed approach has been validated by theoretical derivation and practical experimental researches, and the adaptivity and robustness of the proposed approach are also illustrated. The results of the researches demonstrate the proposed approach is promising in practical applications of bolt Looseness monitoring.
Furui Wang - One of the best experts on this subject based on the ideXlab platform.
-
Monitoring of multi-bolt connection Looseness using a novel vibro-acoustic method
Nonlinear Dynamics, 2020Co-Authors: Furui Wang, Gangbing SongAbstract:Bolted connections are prone to losing their preloads with the increasing service life, thus inducing engineering accidents and economic losses in industries. Therefore, it is important to detect bolt loosening, while current structural health monitoring methods mainly focus on single-bolt joints, whose applications in industries are limited. Thus, in this paper, a novel vibro-acoustic modulation (VAM) method, is developed to detect Looseness of the multi-bolt connection. Compared to traditional VAM, the proposed method uses linear swept sine waves for both low-frequency and high-frequency excitations, which avoids a priori knowledge of the structure. Moreover, the orthogonal matching pursuit method is applied to compress original modulated signals and exclude redundant features. Then, a new entropy, namely the Gnome entropy with acronym gEn , is proposed in this paper. According to simulation analysis, the gEn has better anti-noise capacity and fewer parameters than traditional entropy. Finally, after quantifying the dynamic characteristics of compressed signals to obtain feature sets through the gEn , we feed feature sets into a random forest classifier and achieve Looseness detection of the multi-bolt connection. Moreover, the proposed method in this paper has great potential to detect other structural damages and provides guidance for further investigations on the VAM method.
-
monitoring of multi bolt connection Looseness using entropy based active sensing and genetic algorithm based least square support vector machine
Mechanical Systems and Signal Processing, 2020Co-Authors: Furui Wang, Zheng Chen, Gangbing SongAbstract:Abstract Looseness detection of bolted connections is an essential industrial issue that can reduce the maintenance and repair costs caused by joint failures; however, current loosening detection methods mainly focus on the single-bolt connection. Even though several methods, such as the vibration-based method and electro-mechanical impedance (EMI) method, have been employed to detect multi-bolt Looseness, while they are easily affected by environmental issues. Therefore, the main contribution of this paper is to detect loosening of the multi-bolt connection through the PZT-enabled active sensing method, which has several merits including easy-to-implement, low cost, and good ability of anti-environment disturbance. Since the current indicator of the active sensing, namely the signal energy is insensitive to multiple damages, we developed a new damage index (DI) based on the multivariate multiscale fuzzy entropy (MMFE). Subsequently, the maximum relevance minimum redundancy (mRMR) was used to select significant features from the MMFE-based DI to construct the new datasets. After feeding the new datasets into the genetic algorithm-based least square support vector machine (GA-based LSSVM), we trained a classifier to detect loosening of the multi-bolt connection. Finally, repeated experiments were conducted to demonstrate the effectiveness of the proposed method, which can guide future investigations on bolt Looseness detection.
-
modeling and analysis of an impact acoustic method for bolt Looseness identification
Mechanical Systems and Signal Processing, 2019Co-Authors: Furui Wang, Gangbing SongAbstract:Abstract Bolted joints are fundamental building blocks and have been widely used to hold multiple structural components together, while their Looseness may lead to costly disasters in industries. Compared to current bolt loosening detection methods that are often hampered due to the need for highly experienced personnel or an overly complex sensor-structure interaction, a new percussion-based method using analytical modeling and numerical simulation was proposed to reduce cost and avoid contact-type sensor installation, which is a great contribution. Analytically, the bolted joint was modeled equivalently as a laminated plate by using the virtual material method and the layer-wise theory, and its percussion-induced sound pressure level (SPL) can be obtained via the acoustic radiation mode approach. The corresponding numerical simulation was developed with the focus on the acoustic-structure coupling, and the acoustic boundary conditions were satisfied through a perfectly matched layer (PML). Compared to prior work, another contribution of this paper is that the proposed method further considers the critical effect of bolted interfacial roughness, which affects radiation sound signals significantly. Finally, acoustic tests were carried out, and the good agreement between results of modeling, simulation, and experiments demonstrate the effectiveness of the proposed method. As a rapid and non-invasive bolt Looseness detection method, the investigations in this paper can provide guidance for the future development of bolt Looseness detection methods.
-
bolt early Looseness monitoring using modified vibro acoustic modulation by time reversal
Mechanical Systems and Signal Processing, 2019Co-Authors: Furui Wang, Gangbing SongAbstract:Abstract Structural health monitoring (SHM) of bolted joints has played a vital role in estimation of bolt Looseness and prediction of residual service life of bolted connections, thus saving money and significantly improving the efficiency of maintenance routines across industries. In the past decades, several SHM methods, particularly acoustic/ultrasonic methods, have been used to identify the health status of bolted connections. Compared to the linear ultrasound techniques such as active sensing, the vibro-acoustic modulation (VAM) method that is based on nonlinear ultrasonic features has proven its efficiency in bolt early Looseness monitoring; however, some drawbacks impede its practical use. The main contribution of this paper is to develop a modified VAM (MVAM) that can circumvent existing problems with practical implementation and provide higher sensitivity. First, the shaker used in the traditional VAM was replaced by a piezoceramic transducer to improve its practicality. Moreover, instead of sine waves, linear swept sine signals were used for both low-frequency (LF) pump vibration and high-frequency (HF) probe wave. In other words, no a priori knowledge of the structural condition is needed, which further broadens the scope of application. Subsequently, the time reversal (TR) method was applied to overcome problems including signal energy dissipation and low signal-to-noise ratio (SNR) in traditional VAM. Moreover, the noise-assisted multivariate empirical mode decomposition (NA-MEMD) and multiscale multivariate sample entropy (MMSE) were used to develop a new damage index (DI) for bolt early Looseness monitoring. Finally, multiple repeated experiments were conducted to verify the accuracy of the proposed method and its ability to simplify bolt early Looseness monitoring in terms of practical operation, by comparing the proposed MMSE-based DI with nonlinear DI of traditional VAM method.
-
A Novel Fractal Contact-Electromechanical Impedance Model for Quantitative Monitoring of Bolted Joint Looseness
IEEE Access, 2018Co-Authors: Furui Wang, Siu Chun Michael Ho, Gangbing SongAbstract:Bolted joint are among the key components that enable the robust assembly of a wide variety of structures. However, due to wear and tear over time, bolted joint may loosen, and if not detected in its early stages, can lead to devastating results. A monitoring method that can detect bolted joint Looseness prior to bolt failure will be essential for the continued operation of the host structure and depending on the situation, the safety of the occupants. Prior research has proven the electromechanical impedance method (EMI) to be an effective technique for detecting the loosening of bolted joints, however, EMI-based methods until now are focused on qualitative health monitoring, which can only provide limited information about the damage. Thus, this paper attempts to quantify EMI based methods through the integration of fractal contact theory, the result of which is a novel electromechanical impedance model for quantitative monitoring of bolted Looseness. The method determines the effective impedance of the bolted joint and is applied to develop the relationship between the electrical impedance of a piezoceramic patch installed on the joint and the mechanical impedance of the bolted joint. The mechanical impedance of the bolted joint under various preloads is computed by using the fractal contact theory. Then, the bolted Looseness can be monitored quantitatively. At last, a set of verification tests under different applied preload of bolted joint are conducted to verify the validity of the proposed model in this paper.
Michele J Gelfand - One of the best experts on this subject based on the ideXlab platform.
-
cultural tightness Looseness and perceptions of effective leadership
Journal of Cross-Cultural Psychology, 2016Co-Authors: Mert Aktas, Michele J Gelfand, Paul J HangesAbstract:Previous research has investigated the relationship between cultural values and leadership. This research expands on this tradition and examines how the strength of social norms—or tightness–Looseness—influences perceptions of effective leadership. Data from Gelfand, Raver, et al. were integrated with GLOBE’s leadership research to examine the attributes of leaders seen as leading to effectiveness in tight and loose cultures. Analyses of data across 29 samples show that cultural tightness is positively related to the endorsement of autonomous leadership and negatively related to the endorsement of charismatic and team leadership, even controlling for in-group collectivism, power distance, and future orientation at the societal and organizational level of analysis. Theoretical and practical implications are discussed.
-
tightness Looseness across the 50 united states
Proceedings of the National Academy of Sciences of the United States of America, 2014Co-Authors: Jesse R Harrington, Michele J GelfandAbstract:This research demonstrates wide variation in tightness–Looseness (the strength of punishment and degree of latitude/permissiveness) at the state level in the United States, as well as its association with a variety of ecological and historical factors, psychological characteristics, and state-level outcomes. Consistent with theory and past research, ecological and man-made threats—such as a higher incidence of natural disasters, greater disease prevalence, fewer natural resources, and greater degree of external threat—predicted increased tightness at the state level. Tightness is also associated with higher trait conscientiousness and lower trait openness, as well as a wide array of outcomes at the state level. Compared with loose states, tight states have higher levels of social stability, including lowered drug and alcohol use, lower rates of homelessness, and lower social disorganization. However, tight states also have higher incarceration rates, greater discrimination and inequality, lower creativity, and lower happiness relative to loose states. In all, tightness–Looseness provides a parsimonious explanation of the wide variation we see across the 50 states of the United States of America.
-
the role of culture gene coevolution in morality judgment examining the interplay between tightness Looseness and allelic variation of the serotonin transporter gene
Culture and Brain, 2013Co-Authors: Alissa J Mrazek, Joan Y Chiao, Katherine D Blizinsky, Janetta Lun, Michele J GelfandAbstract:This research provides novel insights into the evolutionary basis of cultural norm development and maintenance. We yield evidence for a unique culture–gene coevolutionary model between ecological threat, allelic frequency of the serotonin transporter polymorphism (5-HTTLPR), cultural tightness–Looseness—the strength of norms and tolerance for deviance from norms—and moral justifiability. As hypothesized, the results across 21 nations show that: (a) propensity for ecological threat correlates with short (S) allele frequency in the 5-HTTLPR, (b) allelic frequency in the 5-HTTLPR and vulnerability to ecological threat both correlate with cultural tightness–Looseness, (c) susceptibility to ecological threat predicts tightness–Looseness via the mediation of S allele carriers, and (d) frequency of S allele carriers predicts justifiability of morally relevant behavior via tightness–Looseness. This research highlights the importance of studying the interplay between environmental, genetic, and cultural factors underlying contemporary differences in social behavior and presents an empirical framework for future research. Electronic supplementary material The online version of this article (doi:10.1007/s40167-013-0009-x) contains supplementary material, which is available to authorized users.
-
on the nature and importance of cultural tightness Looseness
Journal of Applied Psychology, 2006Co-Authors: Michele J Gelfand, Lisa Hisae Nishii, Jana L RaverAbstract:Cross-cultural research is dominated by the use of values despite their mixed empirical support and their limited theoretical scope. This article expands the dominant paradigm in cross-cultural research by developing a theory of cultural tightness-Looseness (the strength of social norms and the degree of sanctioning within societies) and by advancing a multilevel research agenda for future research. Through an exploration of the top-down, bottom-up, and moderating impact that cultural tightness-Looseness has on individuals and organizations, as well as on variance at multiple levels of analysis, the theory provides a new and complementary perspective to the values approach.
Qingzhao Kong - One of the best experts on this subject based on the ideXlab platform.
-
percussion based bolt Looseness monitoring using intrinsic multiscale entropy analysis and bp neural network
Smart Materials and Structures, 2019Co-Authors: Rui Yuan, Qingzhao Kong, Gangbing SongAbstract:In this paper, a novel percussion-based bolt Looseness monitoring approach using intrinsic multiscale entropy analysis and back propagation (BP) neural network is proposed. The percussion-caused audio signals of bolt connection are decomposed by complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) to obtain intrinsic mode functions (IMFs). The IMFs are in order of the high-to-low instantaneous frequencies and contain underlying dynamical characteristic information of audio signals. The multiscale sample entropy (MSE) is improved by smoothed coarse graining process, and the proposed improved multiscale sample entropy (IMSE) values of certain IMFs can be adopted as indicators of different bolt Looseness conditions. The intrinsic multiscale entropy analysis consisting of CEEDMAN and IMSE can properly extract underlying dynamical characteristic information during audio signal processing in bolt Looseness condition identification. The obtained indicators, which are IMSE values at smallest scale factors, were employed as input in BP neural network for training and testing, to achieve accurate and stable bolt Looseness condition monitoring. The effectiveness and superiority of the proposed approach has been validated by theoretical derivation and practical experimental researches, and the adaptivity and robustness of the proposed approach are also illustrated. The results of the researches demonstrate the proposed approach is promising in practical applications of bolt Looseness monitoring.
-
tapping and listening a new approach to bolt Looseness monitoring
Smart Materials and Structures, 2018Co-Authors: Qingzhao Kong, Junxiao Zhu, Gangbing SongAbstract:Bolted joints are among the most common building blocks used across different types of structures, and are often the key components that sew all other structural parts together. Monitoring and assessment of Looseness in bolted structures is one of the most attractive topics in mechanical, aerospace, and civil engineering. This paper presents a new percussion-based non-destructive approach to determine the health condition of bolted joints with the help of machine learning. The proposed method is very similar to the percussive diagnostic techniques used in clinical examinations to diagnose the health of patients. Due to the different interfacial properties among the bolts, nuts and the host structure, bolted joints can generate unique sounds when it is excited by impacts, such as from tapping. Power spectrum density, as a signal feature, was used to recognize and classify recorded tapping data. A machine learning model using the decision tree method was employed to identify the bolt Looseness level. Experiments demonstrated that the newly proposed method for bolt Looseness detection is very easy to implement by 'listening to tapping' and the monitoring accuracy is very high. With the rapid in robotics, the proposed approach has great potential to be implemented with intimately weaving robotics and machine learning to produce a cyber-physical system that can automatically inspect and determine the health of a structure.
-
smart washer a piezoceramic based transducer to monitor Looseness of bolted connection
Smart Materials and Structures, 2017Co-Authors: Linsheng Huo, Gangbing Song, Qingzhao Kong, Dongdong ChenAbstract:The safety of a bolted connection, as one of the most common ways of making two or more parts/components work together in engineering structures, is very important in order to ensure the health of the whole structure. However, bolt loosening or pre-load degradation may induce the failure of the bolt connection, threatening the normal operation of the system's structure. As a result, it would be beneficial if the health condition of the bolt connection could be monitored in real time. In this paper, a 'smart washer', fabricated by embedding a piezoceramic patch into two pre-machined flat metal rings, was invented and then introduced as a transducer to detect the Looseness of a bolted connection. A simple specimen, which consists of two steel plates connected by a nut, a bolt and two smart washers, was fabricated as the test object to study the performance of the 'smart washers' (SWs). For the specimen, a smart washer was used as an actuator to generate a stress wave, and the other one was used as a sensor to detect the propagated wave that traveled through the interface of the bolted connection. A time reversal method was employed to quantify the energy of the stress wave propagating between the two washers, and thus it was possible to build a relationship between the extent of any pre-loaded degradation of the bolt connection and the response signal of the stress wave traveling between the two washers. In addition, a normalized bolt Looseness index was proposed for evaluating the Looseness of a bolt connection based on wavelet energy analysis.
Linsheng Huo - One of the best experts on this subject based on the ideXlab platform.
-
monitoring of bolt Looseness induced damage in steel truss arch structure using piezoceramic transducers
IEEE Sensors Journal, 2018Co-Authors: Tianyong Jiang, Lei Wang, Linsheng Huo, Gangbing SongAbstract:In this paper, we develop a stress wave-based active-sensing approach using piezoceramic transducers to detect the bolt Looseness-induced damage in steel truss arch structures. A specimen of a steel tress arch structure was designed and fabricated. The structure consisted of top chords, bottom chords, Web members, and gusset plates, which were all connected by bolted connections. To implement the active sensing approach, the lead zirconate titanate (PZT) transducer bonded on the gusset plate was used as an actuator to generate stress waves, and the PZT transducers mounted on the other parts, such as top chords, bottom chords, and Web members, were used as sensors to detect the propagated stress waves. Based on the tightness of the bolts, the specimen had three different states: the healthy state, damage state I, and damage state II. The signals received by the PZT sensors were analyzed using the wavelet packet analysis. In addition, the structure stiffness was also considered as a comparative approach in this paper. The experimental results illustrate that when the initial Looseness-induced damage occurs, the structure stiffness is not significantly reduced while the wavelet packet energy changes significantly, revealing the advantage of the proposed approach over the stiffness-based method. These research results demonstrated that the developed piezoceramic-based active-sensing approach has potentials to identify the initial bolt Looseness occurrence for steel truss arch structures.
-
a fractal contact theory based model for bolted connection Looseness monitoring using piezoceramic transducers
Smart Materials and Structures, 2017Co-Authors: Linsheng Huo, Gangbing Song, Furui WangAbstract:In this paper, based on the fractal contact theory, a new analytical model for bolted joints is proposed to monitor bolt Looseness by using a pair of piezoceramic transducers for ultrasonic wave generation and detection. The time reversal method is used to obtain the focused signal peak amplitude during ultrasonic wave propagation through bolt connection surface. The influence of bolt load on the actual contact area of the bolted joint surface is determined by the fractal contact theory, and the finite element method is applied to obtain the relationship between the actual contact area and the focused signal peak amplitude. The focused signal peak obtained through the time reversal method increases with the increase of applied axial load before saturation. The investigation proposed in this paper is based on the inherent contact mechanism between the two contact surfaces, and achieves more accurate quantitative monitoring of bolt Looseness. Finally, a comparison of the predicted and experimental results shown validates the proposed model in this paper.
-
smart washer a piezoceramic based transducer to monitor Looseness of bolted connection
Smart Materials and Structures, 2017Co-Authors: Linsheng Huo, Gangbing Song, Qingzhao Kong, Dongdong ChenAbstract:The safety of a bolted connection, as one of the most common ways of making two or more parts/components work together in engineering structures, is very important in order to ensure the health of the whole structure. However, bolt loosening or pre-load degradation may induce the failure of the bolt connection, threatening the normal operation of the system's structure. As a result, it would be beneficial if the health condition of the bolt connection could be monitored in real time. In this paper, a 'smart washer', fabricated by embedding a piezoceramic patch into two pre-machined flat metal rings, was invented and then introduced as a transducer to detect the Looseness of a bolted connection. A simple specimen, which consists of two steel plates connected by a nut, a bolt and two smart washers, was fabricated as the test object to study the performance of the 'smart washers' (SWs). For the specimen, a smart washer was used as an actuator to generate a stress wave, and the other one was used as a sensor to detect the propagated wave that traveled through the interface of the bolted connection. A time reversal method was employed to quantify the energy of the stress wave propagating between the two washers, and thus it was possible to build a relationship between the extent of any pre-loaded degradation of the bolt connection and the response signal of the stress wave traveling between the two washers. In addition, a normalized bolt Looseness index was proposed for evaluating the Looseness of a bolt connection based on wavelet energy analysis.
