Time Domain Vibration Responses Research Articles

Optimal tuning of three deep learning methods with signal processing and anomaly detection for multi-class damage detection of a large-scale bridge

Long-span bridges play a crucial role in urbanization, connecting communities across vast obstacles. Structural health monitoring techniques have been deployed on these bridges, generate large amounts of data through sensor measurements, requiring data-driven approaches like deep learning (DL) for effective analysis. However, feature extraction from time-domain vibration response signals poses challenges for DL methods. To address this, the study proposes utilizing signal processing techniques such as the multivariate empirical mode decomposition (MEMD) and Wavelet transform (WT) to extract essential features for damage classification. The incorporation of MEMD and WT aims to overcome limitations and process nonstationary and nonlinear signals effectively. Three DL techniques, long-short-term memory (LSTM), one dimensional convolutional neural network (1D-CNN), multi-layer perceptron (MLP) are tuned and applied to Structural Health Monitoring of Tianjin Yonghe Bridge (located in China) as a real-world case study, in order to detect its condition by Deep signal anomaly detection and identify types of the damage. A powerful meta-heuristic algorithm called Observer-Teacher-Learner-Based Optimization, is used to optimize both hyperparameters and architecture of each DL models. The results demonstrate that the optimally tuned DLs are successful in identifying types of damage, as well as the condition of the structure, for the Tianjin Yonghe Bridge. The average accuracy values are obtained as 98.13, 97.96, and 97.79 for 1D-CNN, LSTM, and MLP, respectively. Such optimally tuned DLs are evaluated as effective solutions for detecting damage on large-scale bridges by extracting statistical time-domain and time–frequency domain features using the WT and MEMD.

A 2D-CNN-Based Two-Stage Structural Damage Localization and Quantification Technique Using Time Domain Vibration Data

The conventional approaches for detecting structural degradation are time-consuming, labor-intensive, and costly. The physical monitoring of the structure also poses risks to the health and safety of supervisors. Therefore, damage estimation of any structure using artificial intelligence (AI), more specifically deep learning (DL), is becoming more significant in civil infrastructure. In the presented research article, an efficient two-stage damage detection method is proposed for structural damage detection (SDD) from time domain vibration signals. The proposed method utilizes two-dimensional convolutional neural network (2D-CNN) architecture as a DL algorithm for damage detection. Here, a computer-aided damage detection method for steel beam and frame-type structures is developed using 2D-CNN algorithm in the Google Colab platform. The effectiveness of the proposed method is first verified, and it provides more than 90% accuracy for identifying the damage location and severity of a cantilever beam for single- and multi-damage scenarios from numerically simulated noisy displacement data. The algorithm is also experimentally validated through the raw acceleration data of damaged steel frame joints collected from the Qatar University Grandstand simulator (QUGS). The proposed 2D-CNN algorithm performs better than other DL algorithms by achieving 100% accuracy within 10 epochs for damage detection of steel frames using QUGS data. It demonstrates significant potential for detecting damage location and quantifying damages for single- and multi-damage scenarios using noise-free and noisy datasets. The primary contribution of this study resides in the implementation of two-stage damage detection algorithm utilizing 2D-CNN with time domain vibration response for multiclass damage identification and quantification.

Dynamics Modeling and Analysis of Rolling Bearings Variable Stiffness System with Local Faults

By analyzing the support of load-carrying rolling elements when the rolling elements fall into the fault position, the dynamics model of a rolling bearing variable stiffness system with local faults is proposed, considering the retention factor of the contact deformation. Then, this paper researches the change of effective contact stiffness, contact deformation, contact force, and the total effective stiffness of the rolling elements. The results show that the contact stiffness of the rolling elements abruptly decreases when the rolling elements fall into the fault position. The contact deformation and contact force of the load-carrying rolling elements in the load zone increase, rebalancing the external radial load while causing a sudden reduction in the total effective stiffness, resulting in the vibration of the system. When different rolling elements fall into the outer ring fault position, the change in total effective stiffness and the system response are equal in magnitude. Additionally, there is a significant outer race fault characteristic frequency accompanied by frequency multiplication in the fault characteristic spectrums. When different rolling elements fall into the inner race fault position, the total effective stiffness is modulated by the inner race rotation and varies dramatically, resulting in the amplitude of the system time domain vibration response also being modulated by the inner race rotation and varying dramatically. Additionally, there is a significant inner race rotational frequency accompanied by frequency multiplication, an inner race fault characteristic frequency accompanied by frequency multiplication, and a side frequency in the fault characteristic spectrums. The research can provide some reference for the effective diagnosis of the rolling bearing fault.

Theoretical and Experimental Studies on Vibration Resistance of Composite Plates with Damping Coating

Abstract: This study performs both theoretical and experimental studies on the vibration resistance of composite plates with damping coating subjected to impulse excitation load. A dynamic model is first proposed and the key differential equations are derived to solve the natural frequencies, time-domain vibration response, and dynamic stiffness at any vibration response point regarding the excitation point of such a coated structure. Then, a dynamic experiment system of two plate specimens with and without DC knocked by a hammer excitation is set up. The measured data indicates that the proposed dynamic model is trustworthy for predicting natural frequencies and dynamic stiffness results. Furthermore, based on the calculated dynamic stiffness data associated with the first four modes, the anti-vibration contribution of DC is quantitatively evaluated. It can be found that the coating can indeed improve the vibration resistance of the structure by up to 74.7%. In addition, the vibration suppression effect of DC is found to be closely related to the mode order of such a structure as well as the selected boundary condition.

Vibro-impact response of FRP sandwich plates with a foam core reinforced by chopped fiber rods

In the present study, both the impact and vibration response characteristics of fiber reinforced polymer (FRP) sandwich plates (FRPSPs) with a foam core (FC) reinforced by chopped fiber rods (CFRs) are investigated. Initially, a dynamic model is proposed to predict the vibro-impact characteristics of the FC-CFRs-FRPSP structures. Here, by considering the influence of the dispersion pattern of chopped fiber rods, the equivalent material parameters of this complex core are redefined. Also, by employing the modified mid-plane displacement equation based on the principle of virtual work at the impact point, together with the progressive quasi-static approach and Reddy's high-order shear deformation principle, the key parameters such as impact contact force and displacement related to each failure event are obtained. In addition, with consideration of the impact damage, the natural frequencies and vibration responses are solved by using the energy principle, the proportional damping method, and the Duhamel integral technique. Finally, a number of the FC-FRPSP specimens with and without reinforcement of CFRs are fabricated and tested under different impact energies for verifying the present model. Also, the influences of critical geometric and material parameters on the vibro-impact response of the FC-CFRs-FRPSP structures are discussed. It has been found that the FC-CFRs-FRPSP specimens have a smaller vibro-impact response compared to the specimens without CFRs. For example, when impact energy of 10 J is applied, the impact peak force increases by 19.1%, the impact displacement reduces by 26.6%, and the maximum time-domain vibration response reduces by 5.8%. To reduce the vibro-impact response of such structures, it is recommended to adopt a large thickness ratio of the CFR reinforced foam core to the overall sandwich plate as well as volume fraction of CFRs to the foam core with a uniform dispersion pattern.

Influence analysis of control signal phase on the vibration reduction effect of active constrained layer damping

The phase of the control signal applied on the piezoelectric constrained layer will have a direct influence on the vibration reduction effect in the process of implementing active constrained layer damping (ACLD) to the structure. Taking the ACLD cantilever beam system as the object, this paper focused on the study of the effect of control signal phase on the vibration suppression using the ACLD by establishing the experimental system and creating the relevant dynamic model. By analyzing the shear deformation of viscoelastic layer and combining piezoelectric equation, dynamic viscoelastic theory and mechanical analysis, a dynamic model of ACLD cantilever beam was created, which can effectively simulate two damping mechanisms and include the influence of control signal phase. The rationality of the dynamic model was verified by comparing the natural frequency and the time-domain vibration response corresponding to different control signal phases obtained by simulation and experiment. Using the presented dynamic model and the experimental results, the influence of the control signal phase on the vibration reduction effect was determined. Specifically, the control signal phase and the vibration response amplitude of the cantilever beam show a harmonic relationship centered on the response amplitude without control. The phase value corresponding to the best vibration reduction effect is not 180° like pure piezoelectric active vibration reduction and it is about 140° because of the hysteresis effect of viscoelastic material (for ZN-1 viscoelastic material selected in this study, the loss angle is about 40°).

Effect of delayed resonator on the vibration reduction performance of vehicle active seat suspension

The combination of dynamic vibration absorber and partial state feedback with time-delay is called delayed resonator. In order to suppress the seat vibration caused by uneven road surface and improve ride comfort, the delayed resonator is applied to the seat suspension to realize active control of the seat suspension system. The dynamic model of the half-vehicle suspension system is established, and the time-delay differential equation of the system under external excitation is solved by the precise integration method. The root mean square of the time-domain vibration response of seat displacement, seat acceleration and vehicle acceleration are selected as the objective function. Then, the optimal time-delay control parameters are obtained by particle swarm optimization algorithm. The frequency sweeping method is used to obtain the critical time-delay value and time-delay stable interval of the system. Finally, an active seat suspension model with delayed resonator is established for numerical simulation. The results show that the delayed resonator can greatly suppress the seat vibration response regardless of the road simple harmonic excitation or random excitation. Compared with dynamic vibration absorber, it has a better vibration absorption effect and a wider vibration reduction frequency band.

Densely connected convolutional networks for vibration based structural damage identification

Vibration-based damage identification has been a challenging task in structural health monitoring. The main difficulty lies on the reliable correlation between the measured vibration characteristics and damage states (e.g., stiffness reductions) of structures. Such states can ideally indicate the presence, locations, and severities of structural damages. The procedure is considered as a feature extraction process from the input measurement, mapping the selected features to damage states. Time domain vibration responses, e.g., acceleration responses, are used in this study for damage identification. To address this pattern recognition problem, many methods have been developed including various neural networks in recent years. This paper proposes a novel approach based on densely connected convolutional networks (DenseNets), which is one of the major breakthroughs in the computer vision community, for vibration based structural damage identification. It implements dense connectivity in the convolutional neural network architecture, which fits well for this study using acceleration responses. Both low-level and high-level features are learned and reused during training. It not only eases the information flow during training, but also preserves all levels of features and tends to be more effective for damage identification. Besides, the dense connectivity alleviates the gradient vanishing problem and strengthens feature propagation through the network. In the meantime, these designs substantially reduce the number of parameters, making the network easy to train. The performance of the proposed approach is evaluated through both numerical and experimental verifications. Both modelling uncertainties and measurement noises are considered in numerical studies. The results from numerical and experimental studies demonstrate that the damage localization and quantification are achieved with high accuracies (e.g., Regression value ≥ 96.0% on numerical datasets, and ≥ 94.9% on experimental datasets) and good robustness.

A machine learning approach for vibration-based multipoint tool insert health prediction on vertical machining centre (VMC)

A cutting tool condition is always considered as a key contributor to the machining operation. In-process failure of the tool directly affects the surface roughness of a workpiece, the power consumption of prime mover, and endurance of the process, etc. Thus supervisory system envisioning its health prediction is drawing industry attention. This needs to be adopted by a framework which institutes knowledge built data with the intent to predict defects earlier and prevent it from failure. In this context, the application of ‘Machine Learning’ (ML) methodology would assist the classification of tool condition and its prediction. In an attempt to monitor the multipoint tool insert health, an ML-based approach is presented in this paper. The time-domain vibration response for defect-free and various faulty configurations of four insert tool were collected during face milling performed on a vertical machining center (VMC). Further statistical features were extracted by designing an event-driven algorithm in Visual Basic Environment (VBE). Features exhibited in the Decision Tree (DT) generated by the J48 algorithm serve as ‘most significant’ amongst all extracted features; hence were selected for further classification. Finally, various tool conditions were categorized using six different ‘supervised-tree-based’ algorithms and a comparative study is presented to find the best possible classifier.

Fault detection in rotating machinery by using the modal state observer approach

The existence of cracks in rotating shafts can lead to failures, which imply economic losses and security issues. In the last decades, attention has been devoted to this subject leading to the development of vibration-based structural health monitoring techniques. In this paper, a fault detection methodology based on the so-called modal state observer is applied for detecting transversal cracks in a horizontal rotating shaft. A rotor composed by a flexible horizontal shaft, two rigid discs, and two self-aligning ball bearings is used. The Luenberger state observer is formulated in the modal domain to estimate the rotor vibration responses described in the modal domain. Consequently, the most affected vibration modes due to the crack existence can be determined. The kernel density estimator is applied to quantify the influence of a crack over the dynamic behavior of the rotor. The time domain vibration responses measured directly on the rotating machine are used for comparison purposes. Numerical and experimental investigations are presented by considering both breathing and open cracks. The breathing behavior of the crack is simulated according to the Mayes model, in which the crack transition from fully open to fully closed is described by a cosine function. The additional flexibility introduced in the shaft by the crack is determined by using the linear fracture mechanics theory. The obtained results demonstrated that the methodology conveyed represents a good alternative technique to detect faults in rotating machines.

Analytical investigation on tire dynamics by rigid–elastic coupled tire model with nonlinear sidewall stiffness

With the means of rigid-elastic coupled tire model, the in-plane vibration characteristic of heavy truck tire is investigated and the time-domain vibration response with the proposed tire model is discussed. With the means of finite difference method, rigid–elastic coupled tire model is developed from flexible beam on elastic foundation tire model and the nonlinear radial stiffness of sidewall is derived and related with the inflation pressure and geometrical feature of sidewall curved arc. In-plane vibration characteristic of heavy truck tire, including transfer function and modal parameters is investigated by experimental hammer test. Taking the error between the analytical and experimental modal frequency as the object value, Genetic Algorithm is utilized to identify the un-known structural parameters. In-plane time-domain dynamics response of heavy truck tire utilizing the proposed tire model with linear/nonlinear sidewall radial stiffness is researched and compared with experimental result. Experimental and theoretical results shows that in-plane rigid–elastic coupled tire model with nonlinear sidewall stiffness can be used to better the precision on predicting the vibration feature excited by the random irregular signal. Rigid–elastic coupled tire model with nonlinear sidewall stiffness can be extended to other heavy truck tire with a large section ratio or tires under impulsive loading conditions.

Influence of different frequencies of axial cyclic loading on time-domain vibration response of the lumbar spine: A finite element study

Very few studies have quantitatively analyzed influence of the loading frequency on time-domain vibration response of the whole lumbar spine in the presence of a physiologic compressive preload. In this study, a three-dimensional non-linear finite element model of ligamentous L1–S1 segment was developed to predict time-domain dynamic response of the whole lumbar spine to axial cyclic loading with different frequencies. A compressive follower preload of 400 N was applied to the model to simulate the physiologic compressive load. Modal analysis was initially performed to extract axial resonant frequency of the model under a 40 kg upper body mass and the 400 N preload. The result showed that the axial resonant frequency was 7.77 Hz. Subsequently, transient dynamic analyses were performed on the model under a sinusoidal axial load of ±40 N at frequencies of 3, 5, 7, 9, 11, 13 and 15 Hz with the 400 N preload and 40 kg mass. The computational results (strains and stresses in the spinal components) were collected and plotted as a function of time. These predicted results were found to be frequency-dependent and consistent with the notion in engineering dynamics texts that the closer the loading frequency approaches the resonant frequency, the larger the response is. For example, the results for 5 Hz load compared to 3 Hz load showed a 68.6–111.5% increase in peak-to-bottom variations of the predicted response parameters, and the results for 13 Hz load compared to 11 Hz load showed a 26.4–37.8% decrease in these variations.

Application of entropy in identification of breathing cracks in a beam structure: Simulations and experimental studies

A cantilever beam with a breathing crack is studied to detect the crack and evaluate the crack depth using entropy measures. During the vibration in engineering structures, fatigue cracks undergo the status from close-to-open (and open-to-close) repetitively leading to a crack breathing phenomenon. Entropy is a measure, which can quantify the complexity or irregularity in system dynamics, and hence employed to quantify the bi-linearity/irregularity of the vibration response, which is induced by the breathing phenomenon of a crack. A mathematical model of harmonically excited unit length steel cantilever beam with a breathing crack located near the fixed end is established, and an iterative numerical method is applied to generate accurate time domain vibration responses. The steady-state time domain vibration signals are pre-processed with wavelet transformation, and the bi-linearity/irregularity of the vibration signals due to breathing effect is then successfully quantified using both sample entropy and quantized approximation of sample entropy to detect and estimate the crack depth. It is observed that the method is capable of identifying crack depths even at very early stages of 3% of the beam thickness with significant increment in the entropy values (more than 200%) compared to the healthy beam. In addition, experimental studies are conducted, and the simulation results are in good agreement with the experimental results. The proposed technique can also be applied to damage identification in other types of structures, such as plates and shells.

Structural damage detection using auto correlation functions of vibration response under sinusoidal excitation

Structural damage detection using time domain vibration responses has attracted more and more researchers in recent years because of its simplicity in calculation and no requirement of a finite element model. This paper proposes a new approach to locate the damage using the auto correlation function of vibration response signals under sinusoidal excitation from different measurement points of the structure, based on which a vector named Auto Correlation Function at Maximum Point Value Vector (AMV) is formulated. A sensitivity analysis of the normalized AMV with respect to the local stiffness shows that under several specific frequency excitations, the normalized AMV has a sharp change around the local stiffness change location, which means that even when the damage is very small, the normalized AMV is a good indicator for the damage. In order to locate the damage, a damage index is defined as the relative change of the normalized AMV before and after damage. Several example cases in stiffness reduction detection of a frame structure valid the results of the sensitivity analysis, demonstrate the efficiency of the normalized AMV in damage localization and the effect of the excitation frequency on its detectability.

Comparative study between the R-ODS and DND methods for damage detection in structures

Measured vibration responses can be processed either in their original time domain or after converting to the frequency domain for the purpose of damage detection. Recently, two new vibration-based methods have been presented separately which successfully identified the location of damage in beam-like structures. One of the methods utilises the vibration responses of cracked structures in time domain and is called deviation from normal distribution (DND). The DND method calculates the difference between actual and normal distribution of vibration responses in time domain to locate cracks. The other method is called residual operational deflection shape (R-ODS) which uses the amplitude and phase of the exciting frequency and its higher harmonics in the frequency domain as a method of crack detection. Previously, these methods were applied only to single cracked beams with sinusoidal excitation and their results were encouraging. Here, the application of the two methods has been extended to multiple cracked beams as well as rotors. Also, the effect of different types of excitations on the detection process using the two methods has been investigated through numerical and experimental examples.

Sensitivity analysis of an auto-correlation-function-based damage index and its application in structural damage detection

Structural damage detection using time domain vibration responses has advantages such as simplicity in calculation and no requirement of a finite element model, which attracts more and more researchers in recent years. In present paper, a new approach to detect the damage based on the auto correlation function is proposed. The maximum values of the auto correlation function of the vibration response signals from different measurement points are formulated as a vector called Auto Correlation Function at Maximum Point Value Vector, AMV for short. The relative change of the normalized AMV before and after damage is used as the damage index to locate the damage. Sensitivity analysis of the normalized AMV with respect to the local stiffness shows that the normalized AMV has a sharp change around the local stiffness change location, which means the normalized AMV is a good indicator to detect the damage even when the damage is very small. Stiffness reduction detection of a 12-story frame structure is provided to illustrate the validity, effectiveness and the anti-noise ability of the proposed method. Comparison of the normalized AMV and the other correlation-function-based damage detection method shows the normalized AMV has a better detectability.

Fault Feature Analysis of a Cracked Gear Coupled Rotor System

Considering the misalignment of gear root circle and base circle and accurate transition curve, an improved mesh stiffness model for healthy gear is proposed, and it is validated by comparison with the finite element method. On the basis of the improved method, a mesh stiffness model for a cracked gear pair is built. Then a finite element model of a cracked gear coupled rotor system in a one-stage reduction gear box is established. The effects of crack depth, width, initial position, and crack propagation direction on gear mesh stiffness, fault features in time domain and frequency domain, and statistical indicators are investigated. Moreover, fault features are also validated by experiment. The results show that the improved mesh stiffness model is more accurate than the traditional mesh stiffness model. When the tooth root crack appears, distinct impulses are found in time domain vibration responses, and sidebands appear in frequency domain. Amplitudes of all the statistical indicators ascend gradually with the growth of crack depth and width, decrease with the increasing crack initial position angle, and firstly increase and then decrease with the growth of propagation direction angle.

SU-D-218-03: Resonant Frequency of Rotating Anode X-Ray Tubes.

To evaluate a new rotating anode X-ray tube from the resonant frequency point of view for stable and safe operation, and to validate a finite element model for insight into X-ray tube rotor dynamics and vibration. The 3-dimensional FEM model of the X-ray tube motor has been developed using ANSYS and COMSOL. The resultant resonant frequency from the FEM simulation is substantiated by experiments. During deceleration of the X-ray tube, an accelerometer and a corresponding amplifier send the time domain vibration response to a spectrum analyzer which generates the power spectrum. In the frequency domain analysis, a peak signifies large vibrations at that frequency. To corroborate the FEM model, the resonant frequency of the motor assembly without the anode attached was also measured. Lastly, a rough estimate of the resonant frequency can also be observed in angular speed curves which are obtained utilizing a quadrature position sensor. The first mode resonance is expected at 20.3 Hz from the FEM simulation. This result matches closely with the peak at 22.2 Hz in the power spectrum and the location of the abrupt decreasing acceleration (slope) in the speed curve at 22 Hz. Without the anode, the FEM simulation result of 35.1 Hz is equal to the first peak at 35.1 Hz, and the angular acceleration is suddenly reduced at 34.4 Hz. For image-guided interventional procedures using a hybrid system, the X-ray tube should create flux at various times requiring repeatedacceleration and deceleration of the motor. Hence it is ideal that the resonant frequency is higher than operational speed, although alternatively the motor could accelerate through the resonant frequency quickly. Design improvements to modify the location of resonance of our motor assemblyare underway using the verified FEM model. NIH R01 EB007626, Richard M. Lucas Foundation.

Theory of inner product vector and its application to multi-location damage detection

Structural damage detection methods using time domain vibration responses have shown appeal in recent years. In previous papers by the authors, the inner product vector (IPV) was proposed as a damage detection algorithm which uses cross correlation functions between vibration responses under white noise excitation or band pass white noise excitation. The proposed algorithm was verified by some simulative and experimental examples featuring a single damage location. However, damage at multiple locations was not considered. Therefore, this paper extends the application of IPV-based structural damage detection to the problem of multiple damage locations. Firstly, the theory of the IPV and its implementation in a damage detection context is reviewed. Then, two strategies for detecting multiple damages utilizing IPV are proposed. Finally, a damage detection experiment of a honeycomb sandwich composite beam is adopted to illustrate the feasibility and effectiveness of the IPV-based damage detection method.

A New Method of Numerical Differential and Time Domain Integral Based on the Analysis of Vibration Response

A new method of numerical differentiation and time domain integral was proposed in this paper, its idea was originated from the analysis of the time domain vibration response. As to numerical differentiation, the discrete sequence could be considered as the displacement response of an one degree-of-freedom system, and the velocity and acceleration response corresponding to the first and second order numerical differentiation. As to time domain integral, the discrete sequence could be considered as the acceleration response of an one degree-of-freedom system, and the velocity and displacement response corresponding to the first and second order time domain integral. All these work were established based on the discretization analysis of Duhamel integral. Numerical simulation result indicates the effective and better accuracy of this new method.