Wave-based Method Research Articles

On a wave-based reduced order model for transient effects computation including mid frequencies

The wave-based computational method named Variational Theory of Complex Rays (VTCR) is revisited in order to improve its robustness and its efficiency to solve transient dynamic problems including medium frequencies. The first problem addressed in the paper concerns the ill-conditioning of wave-based computational approaches. We introduce the concept of “effective portrait” which provides a new framework to the VTCR with a strong reduction of the conditioning number. The second issue deals with the computation over a large frequency bandwidth for which the Proper Generalised Decomposition (PGD) has been retained. A thorough analysis of the efficiency and the limitations of the PGD-VTCR is given. The last issue concerns the synergy between the PGD-VTCR and the exponential window method for solving transient problems.

Axial Stress Measurement of Steel Tubes Using Ultrasonic Guided Waves.

Axially loaded steel tubes are widely used as primary structural members in civil engineering structures. In this paper, a stress measurement method for axially loaded steel tubes is developed based on the linear relationship between the group velocity of guided waves in the steel tube and the stress of the steel tube. The propagation modes of guided waves in a typical steel tube are analyzed using semi-analytical finite element method. A torsional mode T(0,1) is adopted to conduct the measurement. Experiments are carried out to calibrate the linear relationship between the group velocity of guided waves in a steel tube and the stress of the steel tube. The calibrated linear relationship is verified by another round of experiments on the same steel tube specimen. There is an average error of 8.2% between the stresses predicted by the calibrated linear equation and those obtained from strain gauges. Via this study, the guided wave-based stress measurement method has been successfully extended to axially loaded steel tubes.

Localization of a Breathing Delamination Using Nonlinear Lamb Wave Mixing

Abstract A guided wave-based method for localization of breathing delamination is presented in this investigation. The proposed technique utilizes one-way mixing of a dual-frequency fundamental antisymmetric Lamb modes with judiciously selected central frequencies. The dual-frequency interrogation signal, upon interacting with a breathing delamination, leads to additional frequency sidebands in the frequency response spectrum, strength of which is quantified in terms of the combination tone index. The numerical predictions of these sidebands are validated using an in-house experimentation. It is further exposited that the combination tone index depends strongly on the extent of the temporal overlap that the two constituent wave envelopes have as they propagate through the breathing delamination. Accordingly, for a synchronous passage (with 100% temporal overlap), the combination tone index is maximum while it reduces with the decreasing temporal overlap. By utilizing the dispersive nature of the chosen Lamb mode, a relation is then developed correlating the temporal separation of the wave envelopes at the location of the actuator, the group speeds, and the distance between the actuator and the delamination. Based on these inferences, a technique for localizing a breathing delamination is proposed, which involves interrogating the component by systematically altering the temporal overlap in the input waveform and monitoring the combination tone index for its maxima. The efficacy of the localization technique (close to 90%) is demonstrated through an illustrative case analyzed numerically as well as experimentally.

Vibration analysis of double-walled cylindrical shells interconnected with arbitrary connections using a unified semi-analytical method

The vibration characteristics of double-walled cylindrical shells interconnected with arbitrary connections are predicted through a unified semi-analytical method. The motions and displacement fields of inner and outer shells are expressed by Flügge shell theory and wave based method (WBM). To make the present method applicable for arbitrary connections, finite element method (FEM) is adopted to establish their dynamic equations. The coupling with 6 degree of freedoms (DOFs) between the shells and connections are realized using a precise equivalent transformation. Then, a series of artificial springs with 6 DOFs, rather than just 4 DOFs in existing papers, are introduced at each coupling node to achieve general coupling conditions. Through displacement and force continuities between the inner shell, connections and outer shell, the final vibration governing equations are established. Two typical engineering structures, namely double-walled cylindrical shells interconnected by annular plates and splints, are employed to validate the proposed approach. Results show that vibration responses of the shells using the proposed method agree well with the ones presented in literature and calculated through FEM. Furthermore, effects of connecting forms, general coupling and boundary conditions on vibration behaviors are evaluated and several significant phenomena are discovered.

Diffuse Ultrasonic Wave-Based Damage Detection of Railway Tracks Using PZT/FBG Hybrid Sensing System

Damage detection of railway tracks is vital to ensure normal operation and safety of the rail transit system. Piezoelectric sensors, which are widely utilized to receive ultrasonic wave, may be disturbed in the railway system due to strong electromagnetic interference (EMI). In this work, a hybrid ultrasonic sensing system is proposed and validated by utilizing a lead-zirconate-titanate (PZT) actuator and a fiber Bragg grating (FBG) sensor to evaluate damage conditions of the railway tracks. The conventional ultrasonic guided wave-based method utilizing direct wave to detect damages is limited by the complex data analysis procedure and low sensitivity to incipient damage. Diffuse ultrasonic wave (DUW), referring to later arrival wave packets, is chosen in this study to evaluate structural conditions of railway tracks due to its high sensitivity, wider sensing range, and easy implementation. Damages with different sizes and locations are introduced on the railway track to validate the sensitivity and sensing range of the proposed method. Two damage indices are defined from the perspective of energy attenuation and waveform distortion. The experimental results demonstrate that the DUW signals received by the hybrid sensing system could be used for damage detection of the railway tracks and the waveform-distortion-based index is more efficient than the energy-based index.

A novel fault location method for hybrid lines based on traveling wave

In this paper, a novel fault traveling wave-based location method for hybrid lines is proposed. According to the refraction characteristics of fault traveling wave (TW) at junction nodes, the node ratio coefficient value Q is defined based on the amplitude of traveling wave. Then, by comparing the Q values of junction nodes and fault points, a fault section identification principle is proposed to determine the fault line section for hybrid lines. After identification of fault line section, a double-ended fault location method is revised via adding the location compensation factors to mitigate the effect of traveling wave velocity changes on fault location for multi-section hybrid lines. Additionally, considering the detection problems of arrival time for TW signals, the extreme-point symmetric mode decomposition (ESMD) method and Teager energy operator (TEO) are proposed. The ESMD method is applied to decompose the sampled fault traveling wave signals into several intrinsic modes to filter out the fundamental frequency and low frequency signals. The TEO is employed to track the characteristics of TW signals. Effectiveness of the proposed method is validated in PSCAD. Results show that the ESMD-TEO can detect TW signals effectively, and the proposed fault location method can determine the fault line section and locate fault positions correctly.

A new GW-based heteroscedastic Gaussian process method for online crack evaluation

Accurate evaluation of fatigue crack by using structural health monitoring (SHM) methods is very important to the life management of aircraft structures. However, fatigue crack propagation is always a complicated process for individual aircraft structures during their long-term service. And the monitoring has to be performed under different environmental and operational conditions. These factors result in the uncertain distribution of the damage index obtained by SHM. The distribution usually changes along with the service time, which can be defined as heteroscedasticity. The heteroscedasticity characteristic of the uncertain distribution of damage index has an important negative impact on the SHM based diagnostics algorithms if not considered during the evaluation. However, till now, few researchers have considered this important aspect. To improve the evaluation accuracy under different environmental and operational conditions for individual aircraft, this paper proposes a new guided wave-based heteroscedastic Gaussian process method. Gaussian process quantile regression is adopted to estimate the conditional quantiles of the damage index distribution during the service to deal with the heteroscedasticity. The method is validated on an attachment lug fatigue test, an important aircraft structural component. The experimental results demonstrate that the proposed method can quantify the heteroscedastic uncertainty associated and obviously improve the quality of crack evaluation. For the serious heteroscedastic specimen, the maximum evaluation is only 0.7 mm reduced from the original 7.4 mm, which is an order of magnitude.

Vibration mitigation of pile groups by coupling a wave-based vibration analysis and genetic algorithm

ABSTRACT This paper presents a coupled wave-based/genetic algorithm approach for vibration mitigation in a structure built on a pile group. The wave-based method considers the structure and foundation as a whole waveguide system in which the equations of wave propagation at waveguides and wave refraction at discontinuities are solved analytically using Timoshenko beam theory. These solutions are then assembled and solved numerically within a single system matrix. To model the ground, the viscoelastic soil around the piles is modelled using spring-dashpot elements. The wave-based method is used to evaluate a fitness function within a genetic algorithm procedure, and the resulting coupled tool is used for finding the optimal geometric characteristics of a pile group. The obtained results highlight the efficiency of the wave-based approach to be used in heuristic optimization algorithms such as genetic algorithm. In addition, it is observed that the optimal layout of the pile group depends significantly on loading frequency and soil properties.

A Parallel Dissipation-Free and Dispersion-Optimized Explicit Time-Domain FEM for Large-Scale Room Acoustics Simulation

Wave-based acoustics simulation methods such as finite element method (FEM) are reliable computer simulation tools for predicting acoustics in architectural spaces. Nevertheless, their application to practical room acoustics design is difficult because of their high computational costs. Therefore, we propose herein a parallel wave-based acoustics simulation method using dissipation-free and dispersion-optimized explicit time-domain FEM (TD-FEM) for simulating room acoustics at large-scale scenes. It can model sound absorbers with locally reacting frequency-dependent impedance boundary conditions (BCs). The method can use domain decomposition method (DDM)-based parallel computing to compute acoustics in large rooms at kilohertz frequencies. After validation studies of the proposed method via impedance tube and small cubic room problems including frequency-dependent impedance BCs of two porous type sound absorbers and a Helmholtz type sound absorber, the efficiency of the method against two implicit TD-FEMs was assessed. Faster computations and equivalent accuracy were achieved. Finally, acoustics simulation of an auditorium of 2271 m3 presenting a problem size of about 150,000,000 degrees of freedom demonstrated the practicality of the DDM-based parallel solver. Using 512 CPU cores on a parallel computer system, the proposed parallel solver can compute impulse responses with 3 s time length, including frequency components up to 3 kHz within 9000 s.

On the Robustness and Efficiency of the Plane-Wave-Enriched FEM with Variable q-Approach on the 2D Room Acoustics Problem

Partition of unity finite element method with plane wave enrichment (PW-FEM) uses a shape function with a set of plane waves propagating in various directions. For room acoustic simulations in a frequency domain, PW-FEM can be an efficient wave-based prediction method, but its practical applications and especially its robustness must be studied further. This study elucidates PW-FEM robustness via 2D real-scale office room problems including rib-type acoustic diffusers. We also demonstrate PW-FEM performance using a sparse direct solver and a high-order Gauss–Legendre rule with a recently developed rule for ascertaining the number of integration points against the classical linear and quadratic FEMs. Numerical experiments investigating mesh size and room geometrical complexity effects on the robustness of PW-FEM demonstrated that PW-FEM becomes more robust at wide bands when using a mesh in which the maximum element size maintains a comparable value to the wavelength of the upper-limit frequency. Moreover, PW-FEM becomes unstable with lower spatial resolution mesh, especially for rooms with complex shape. Comparisons of accuracies and computational costs of linear and quadratic FEM revealed that PW-FEM requires twice the computational time of the quadratic FEM with a mesh having spatial resolution of six elements per wavelength, but it is highly accurate at wide bands with lower memory and with markedly fewer degrees of freedom. As an additional benefit of PW-FEM, the impulse response waveform of quadratic FEM in a time domain was found to deteriorate over time, but the PW-FEM waveform can maintain accurate waveforms over a long time.

A Novel Ultrasonic Guided Wave-Based Method for Railway Contact Wire Defect Detection

Detection of defects in contact wire is significantly important to railway system. Due to the insensitivity to the deep-seated defects, traditional optics-based methods fail to detect the internal defects of contact wire. To overcome this shortcoming, a new defect detection method based on ultrasonic guided wave is proposed in this paper. Theoretical dispersion curves and wave structures for the TCG-110 contact wire are derived using a special modeling technique called the semi-analytical finite element (SAFE) method. It is shown that the longitudinal-like M3 mode in the frequency range of 50-100 kHz is attractive for the proposed application. Then, the experimental scheme is established based on the pulse-echo configuration to detect the defects in contact wire. The echoes overlapping and drown problems in guided wave signal leading to the time resolution of original signal is too low to extract useful position information of defects. Hence, the sparse deconvolution method is introduced based on the convolution model of guided wave signal and sparse theory, and the time resolution of guided wave signal is significantly improved. The experimental results show that the proposed method can detect the defects in contact wire effectively with high accuracy.

Economical Setting-Free Double-Ended Fault Locator for Transmission Lines: Experiences From Recent Pilot Installations

Locating fault precisely on power transmission line is highly beneficial to utilities and accurate fault location can expedite the repair of the faulted components, speed-up restoration, and reduce outage time. In this paper, a setting-free double ended fault location method for power transmission line is proposed using both end voltage and current measurements. This algorithm estimates the required setting parameters using pre-fault data and fault location is calculated using estimated parameters and during fault data. The proposed method is verified using the EMTDC simulations for lines connected with conventional and inverter-based renewable resources. The method is not affected by the error in line parameters and renewable integration. The method is implemented in Intelligent Electronic Device (IED) using 1kHz sampling rate and successfully installed on a 400 kV, 233.07 km line from Power Grid Corporation of India (POWERGRID), India and on a 220 kV, 265.6 km line from Svenska Kraftnat (SVK), Sweden. This paper presents laboratory test results as well as field experimental results in which line patrolling crews found the actual location. Pilot installation results match the performance demonstrated with laboratory experimental results. The method gives average fault location error of ~ 0.1 %. The method can locate the fault within two-tower span distance (~300m) which is comparable with traveling wave-based method that requires 1000 times higher sampling rate, high-cost hardware, more complex commissioning, and settings. These geographically diverse pilot installation results stand as testimony to the fault location accuracy of the proposed setting-free fault location solution.

Negative Pressure Wave-Based Method for Abnormal Signal Location in Energy Transportation System

Abnormal signal location is an indispensable part to handle unexpected events such as pipeline leak in energy transportation system. However, unclear signal characteristics would make traditional location methods such as wavelet analysis failure in location process. To address it, a data-driven method based on negative pressure wave (NPW) is proposed in this article. First, a signal enhancement model based on Gaussian process regression (GPR) is proposed to highlight the changed signal characteristics. Then, a multi-objective evolutionary computation method is proposed to obtain the location result, which overcomes the shortcoming of unclear signal characteristics. Moreover, the signal transmission attenuation rules are added into the location process, which ensures the rationality and the reliability of the location result. Without introducing extra signal numbers and types, the proposed method could achieve higher accuracy and more robustness than traditional location methods such as wavelet analysis, which has the less 1.2% location deviation of the pipeline. Finally, different experiment results show that the proposed method is a realistic way to provide the position of abnormal signal source.

Effects of non-axisymmetric internal structures on vibro-acoustic characteristics of a submerged cylindrical shell using wavenumber analysis

Non-axisymmetric structures (foundations, equipment etc.) have been extensively arranged in axisymmetric shells and proved to change the mechanism of vibration and sound radiation of the shell. To study the effect of non-axisymmetric internal structures, a hybrid analytic-numerical method is developed for vibro-acoustic characteristics analyses of a submerged cylindrical shell. The wave based method (WBM) and finite element method (FEM) are respectively employed to model the shell and internal structures. A precise coupling is carried out to assemble the shell and internal structures, which fully considers all six degree of freedoms (DOFs) at junctions between the two substructures. The acoustic pressure is described by the Helmholtz integral equation. According to the axisymmetric property of the shell, the surface integral is reduced into the curve integral. Subsequently, the final vibro-acoustic model is obtained by introducing the acoustic pressure into the dynamic equation of the coupled structure. The high accuracy of the present method is firstly demonstrated by FEM and boundary element method (BEM). Then by comparing vibro-acoustic responses of the shell with and without internal structures in wave domain, the effects of non-axisymmetric internal structures on vibro-acoustic characteristics of the shell are discussed.

Sound Insulation of Corrugated-Core Sandwich Panels: Modeling, Optimization and Experiment.

With the extension of the applications of sandwich panels with corrugated core, sound insulation performance has been a great concern for acoustic comfort design in many industrial fields. This paper presents a numerical and experimental study on the vibro-acoustic optimization of a finite size sandwich panel with corrugated core for maximizing the sound transmission loss. The numerical model is established by using the wave-based method, which shows a great improvement in the computational efficiency comparing to the finite element method. Constrained by the fundamental frequency and total mass, the optimization is performed by using a genetic algorithm in three different frequency bands. According to the optimization results, the frequency averaged sound transmission of the optimized models in the low, middle, and high-frequency ranges has increased, respectively, by 7.6 dB, 7.9 dB, and 11.7 dB compared to the baseline model. Benefiting from the vast number of the evolution samples, the correlation between the structural design parameters and the sound transmission characteristics is analyzed by introducing the coefficient of determination, which gives the variation of the importance of each design parameter in different frequency ranges. Finally, for validation purposes, a sound insulation test is conducted to validate the optimization results in the high-frequency range, which proves the feasibility of the optimization method in the practical engineering design of the sandwich panel.

Guided wave propagation analysis in stiffened panel using time-domain spectral finite element method

Stiffened panels have been widely utilized in fuselages and wings as critical load-bearing components. These structures are prone to be damaged under long-term and extreme loads, and their health monitoring has been a common concern. The guided wave-based monitoring method is regarded as an efficient approach to detect the damage in stiffened plates because of its wide monitoring range and high sensitivity to micro-damage. Efficient simulation of wave propagation can theoretically demonstrate the detection mechanism of the method. In this study, a Time-Domain Spectral Finite Element Method (TD-SFEM) is adopted to study the wavefield in stiffened plates, where continuous Absorbing Layers with Increasing Damping (ALID) strategy is proposed to circumvent the disturbance of reflected waves on boundaries. After the convergence analysis, the developed TD-SFEM with ALID is validated by the finite element method first. Then, wave scattering and the influence of the stiffener are investigated in detail by comparing the results with the non-stiffened structure. Finally, the effects of the parameters of the stiffener, such as the height and width, on wave propagation are studied, respectively. The results illustrate that the proposed TD-SFEM with ALID is an efficient approach to study the wave propagation in the stiffened plate and can reveal the mechanism of influence of the stiffener. It is found that the height of the stiffener changes the interference of wavefield in the plate, while the effects of the width are mainly in wave scattering and mode conversion.

Ultrasonic and acoustic pulse velocity methods for nondestructive detection of early decay in wood poles

Wood poles are widely used to support overhead distribution and transmission power lines in North America and the world. These poles are vulnerable to internal deterioration due to extreme weather conditions, requiring a large number of poles to be inspected every year. This paper presents a comparative study of four stress wave-based nondestructive testing (NDT) methods commonly used for condition assessment of wood poles. These include the traditional approaches of sounding, sonic pulse velocity, and ultrasonic pulse velocity tests; and a new approach that considers the orthotropic characteristics of wood, uncertainties in the elastic properties, ultrasonic wave velocity and attenuation. Two poles with an internal hole of 4% of the cross-section are evaluated and compared by each method. Ultrasonic measurements of wave velocity and attenuation considering orthotropic characteristics of wood and uncertainties in the elastic properties provide a reliable wave-based NDT method for the detection of early decay in wood poles.

Modeling microperforated panels and permeable membranes for a room acoustic solver with plane-wave enriched FEM

Plane-wave-enriched finite element method (FEM), an efficient wave-based prediction method, uses shape functions incorporating a set of plane waves propagating in various directions to enhance the sound field approximation capability. The method can be an efficient wave-based acoustic solver for room acoustic simulations because it can simulate wave phenomena in rooms accurately with markedly fewer finite elements in spatial discretization than those used for standard FEM. However, several aspects remain to be addressed before its use for practical room acoustic simulations. Accurate sound absorber modelings able to address their frequency and incident angle dependence of absorption characteristics present extremely important issues. This paper presents a proposal of a method of implementing an extended-reaction model of microperforated panel (MPP) and permeable membrane (PM) sound absorbers into a room acoustic solver with plane-wave-enriched FEM. First, we demonstrate the validity of the proposed method in comparison with theoretical values in which impedance tube problems including three sound absorbers composed of MPP and PM are used. Then, the effectiveness over standard FEM is demonstrated via 2D real-scale office problems with the three MPP-PM sound absorbers.

Bolt looseness detection using SH guided wave and wave energy transmission

Lap joints are commonly used in civil infrastructure and mechanical assembly structures. Detecting the connection status of bolts, particularly in the early stages of use, is critical for ensuring structural integrity. A shear horizontal (SH) guided wave-based bolt looseness detection method, excited by a magnetostrictive patch transducer (MPT), is presented in this paper. A normalised bolt-looseness index was proposed based on the wave energy transmission theory by analysing the signals received at the transducer for the transmitted wave passing through the actual contact area and the transducer for the direct incoming wave. Numerical and experimental studies were conducted on a lap joint with four bolts. The relationship between the and bolt loads was obtained, verifying the effectiveness of this method for detecting the extent of the bolt looseness under various bolt tightness states. The results also show that SH0 waves, excited by an MPT, have better detection capability than Lamb waves, when the surface of the lap joint is subjected to liquid medium such as water and professional paint for bridges.

Debonding damage detection of the CFRP-concrete interface based on piezoelectric ceramics by the electromechanical impedance method

Debonding in carbon fiber reinforced polymer (CFRP)-strengthened RC structures might always carry the risk of structural collapse. Several studies have focused on the debonding detection of CFRP-strengthened RC structures by nondestructive methods, which represents some limitations. Therefore, an electromechanical impedance (EMI) method based on piezoelectric ceramic (PZT) was applied to detect damage at the CFRP-concrete interface. First, different simulated interfacial defects in a CFRP sheet-wrapped concrete column were detected, and the feasibility of the method was validated. Then, the debonding process of a CFRP plate strengthened RC beam under four-point loading was monitored by the EMI method. Two damage indices, the root mean square deviation (RMSD) and the mean absolute percentage deviation (MAPD), were used to quantify the degree of damage at the CFRP-concrete interface. It is verified that these two damage indices obtained from the EMI method can clearly capture the process of damage development. Moreover, compared to the wave-based method, the EMI method is more sensitive to incipient concrete and debonding damage, which confirms the practicability of the EMI method for on-site applications.