Tool For Nondestructive Evaluation Research Articles

Rice Leaf Nitrogen Content Estimation Through A Methodological Framework Using Single-Sensor Multispectral Images

Using non-destructive evaluation tools based on imaging techniques, including single-sensor multispectral cameras, provides a cost-effective solution for optimizing rice nitrogen fertilization through site-specific nutrient management. However, their accuracy and precision have been identified as areas for improvement. This study aims to develop a methodology to improve the accuracy of estimations through field experiments. It utilizes multispectral images captured by MAPIR Survey3W Orange Cyan Near-Infrared and MAPIR Survey3W Red Edge cameras. The Normalized Difference Vegetation Index and Red Edge values derived from these images are correlated with Soil Plant Analysis Development values to assess rice nitrogen levels. A prediction model is then built using the Support Vector Regression algorithm. Findings from the experiments underscore the importance of addressing shadow effects, integrating the dataset on light intensity and image capture time, conducting radiometric calibration, filtering outlier data, employing image segmentation, and utilizing nonlinear Canova tests to enhance estimation accuracy. By configuring the Support Vector Regression model with RBF kernel, gamma set to 1.24, and epsilon set to 0.1, the R2 of the train data and validation data reaches 0.851, and 0.840 respectively. Meanwhile, the R2 of the test data achieves 0.793 with a mean absolute percentage error of 3.49 % and a root mean square error of 1.70. These findings underscore the potential of the proposed methodology to improve the estimation of rice nitrogen status based on single-sensor multispectral images, paving the way for more effective nutrient management strategies in rice cultivation.

Damage source localisation in complex geometries using acoustic emission and acousto-ultrasonic techniques: an experimental study on clear aligners

Passive non-destructive evaluation tools such as acoustic emission (AE) testing and acousto-ultrasonics (AU) approach present a complex problem in damage localisation in complex and nonhomogeneous geometries. A novel AU-guided AE frequency interpretation approach is proposed in this research work which aims at overcoming this limitation. For the experimental evaluation, the damage sources from a geometrically complex clear dental aligners are tested under cyclic compression load and their origins are evaluated. Despite the rapid worldwide diffusion of the clear aligners, their mechanical behaviour is poorly investigated. In this work, the frequency characteristics of the artificially simulated stress wave, generated from different dental positions of the clear aligners, are studied using the AU approach. These frequency characteristics are then used to analyse the AE signals generated by these aligners when subjected to cyclic compressive loading. In addition, the time domain characteristics of the AE signals are studied using their Time of Arrival (ToA). The Akaike Information Criterion (AIC) is used to estimate the ToA. These frequency and time domain characteristics of the AE signals are used to estimate the local damage origin in the clear dental aligners. This will help in identifying localised damage sources during the usage period of the aligners. Experimental results revealed significant damages in the left maxillary premolar and right maxillary third molar of the aligners.

Learning Scatter Artifact Correction in Cone-Beam X-Ray CT Using Incomplete Projections with Beam Hole Array

X-ray cone-beam computed tomography (CBCT) is a powerful tool for nondestructive testing and evaluation, yet the CT image quality can be compromised by artifact due to X-ray scattering within dense materials such as metals. This problem leads to the need for hardware- and software-based scatter artifact correction to enhance the image quality. Recently, deep learning techniques have merged as a promising approach to obtain scatter-free images efficiently. However, these deep learning techniques rely heavily on training data, often gathered through simulation. Simulated CT images, unfortunately, do not accurately reproduce the real properties of objects, and physically accurate X-ray simulation still requires significant computation time, hindering the collection of a large number of CT images. To address these problems, we propose a deep learning framework for scatter artifact correction using projections obtained solely by real CT scanning. To this end, we utilize a beam-hole array (BHA) to block the X-rays deviating from the primary beam path, thereby capturing scatter-free X-ray intensity at certain detector pixels. As the BHA shadows a large portion of detector pixels, we incorporate several regularization losses to enhance the training process. Furthermore, we introduce radiographic data augmentation to mitigate the need for long scanning time, which is a concern as CT devices equipped with BHA require two series of CT scans. Experimental validation showed that the proposed framework outperforms a baseline method that learns simulated projections where the entire image is visible and does not contain scattering artifacts.

Detection of indentation damage in carbon fiber/epoxy composites via EIT during the application of bending loads

Electrical impedance tomography (EIT) is a method of spatially mapping the conductivity distribution of a domain and has been studied as a potential embedded sensing or nondestructive evaluation (NDE) tool. An often touted advantage of EIT is that it can be used in-situ; that is, because the method only requires the application of unobtrusive electrodes, it can conceivably be used while the component or structure is in operation. This material-as-the-sensor philosophy strongly aligns with key components of the NDE 4.0 vision such as the realization of intelligent cyber–physical systems (CPS) and digital twins. To date, however, the claim of in-situ sensing via EIT has not been significantly substantiated. This is problematic because operational loads induce strains that often change the conductivity of the material. Establishing that EIT can detect damage-induced conductivity changes through the presence of unrelated strain-induced conductivity changes is therefore important. To that end, we herein study the application of EIT for detecting indentation damage in a carbon fiber/epoxy composite as the composite is loaded in a four-point bend. It was found that the bending load changes the contact impedance of the electrodes, which resulted in poor EIT images when solving the EIT inverse problem with the ℓ2-norm on the error term. Using the ℓ1-norm on the error term, solved via the primal–dual interior point method (PDIPM), significantly improved image quality. Image quality was even further improved through the use of a mixed prior for regularization, and EIT images were compared to thermography with good agreement. These results show that EIT can indeed detect damage through the presence of an applied load, but care must be taken to account for factors such as outlier data arising from electrode degradation and changing contact impedance. Use of the ℓ1-norm on the error term is therefore highly recommended for in-situ imaging via EIT.

Improved detection of nonlinear waves in thin solid materials using a pulse-echo method based on nonlinear modeling of wave fields

The nonlinearity parameter is a powerful tool for nondestructive evaluation, as it provides a measure of the state of damage of structural components. When carrying out nonlinearity parameter measurements of solid structures, the pulse-echo method is more suitable than the through-transmission method; however, a planar stress-free boundary is known to destructively alter the nonlinear wave generation process, including the second harmonic component, meaning that the pulse-echo nonlinear method is limited for practical applications, especially for thin solids. In this work, an improved detection method is proposed for the enhancement of nonlinear wave measurement in thin solids using a pulse-echo method with a dual-element transducer consisting of an outer ring transmitter and an inner disk receiver. A multi-Gaussian beam model is developed for the ring transmitter to fast simulate the pulse-echo nonlinear wave fields, and based on the results, improvements for the received nonlinear waves are achieved by optimizing the driving frequency. The advantages of the proposed method are that solid samples with different thicknesses can be evaluated using a dual-element transducer, and a high measurement accuracy can also be achieved for thin solid samples. Experiments are performed to investigate the harmonic waves measured in fatigue-damaged thin steel samples, and the results verify the effectiveness of the proposed method.

Utilization of Synthetic Near-Infrared Spectra via Generative Adversarial Network to Improve Wood Stiffness Prediction.

Near-infrared (NIR) spectroscopy is widely used as a nondestructive evaluation (NDE) tool for predicting wood properties. When deploying NIR models, one faces challenges in ensuring representative training data, which large datasets can mitigate but often at a significant cost. Machine learning and deep learning NIR models are at an even greater disadvantage because they typically require higher sample sizes for training. In this study, NIR spectra were collected to predict the modulus of elasticity (MOE) of southern pine lumber (training set = 573 samples, testing set = 145 samples). To account for the limited size of the training data, this study employed a generative adversarial network (GAN) to generate synthetic NIR spectra. The training dataset was fed into a GAN to generate 313, 573, and 1000 synthetic spectra. The original and enhanced datasets were used to train artificial neural networks (ANNs), convolutional neural networks (CNNs), and light gradient boosting machines (LGBMs) for MOE prediction. Overall, results showed that data augmentation using GAN improved the coefficient of determination (R2) by up to 7.02% and reduced the error of predictions by up to 4.29%. ANNs and CNNs benefited more from synthetic spectra than LGBMs, which only yielded slight improvement. All models showed optimal performance when 313 synthetic spectra were added to the original training data; further additions did not improve model performance because the quality of the datapoints generated by GAN beyond a certain threshold is poor, and one of the main reasons for this can be the size of the initial training data fed into the GAN. LGBMs showed superior performances than ANNs and CNNs on both the original and enhanced training datasets, which highlights the significance of selecting an appropriate machine learning or deep learning model for NIR spectral-data analysis. The results highlighted the positive impact of GAN on the predictive performance of models utilizing NIR spectroscopy as an NDE technique and monitoring tool for wood mechanical-property evaluation. Further studies should investigate the impact of the initial size of training data, the optimal number of generated synthetic spectra, and machine learning or deep learning models that could benefit more from data augmentation using GANs.

Non-destructive visualization of internal structural changes in humidified magnesium oxide tablets using X-ray computed tomography

Detailed examinations of the internal structure of tablets are imperative for comprehending their formulation, physical attributes, and ensuring their safe utilization. While X-ray computed tomography (CT) is valuable for noninvasively analyzing internal structural changes, the influence of humidity on these structural changes remains unexplored. Accordingly, we aimed to assess the viability of X-ray CT in non-destructively evaluating the internal structure of humidified magnesium oxide (MgO) tablets. MgO tablets were subjected to conditions of 40 °C and 75% humidity for 7 days, weighed pre- and post-humidification, and subsequently stored at room temperature (22–27 °C) until day 90. Their internal structure was evaluated using X-ray CT. We observed a substantial increase in the weight of MgO tablets concomitant with moisture absorption, with minimal changes observed upon storage at room temperature. The skewness reduced immediately post-moisture absorption, remained almost the same post-storage at room temperature, and failed to revert to pre-humidification levels during the storage period. These findings highlight the utility of X-ray CT as an effective tool for non-destructive, three-dimensional, and detailed evaluation of internal structural transformations in MgO tablets.

Structural integrity and healing efficiency study of micro-capsule based composite materials via 1H NMR relaxometry

In this work we present a novel approach utilizing nuclear magnetic resonance (NMR) relaxometry to assess the structural stability of microcapsules employed as self-healing agents in advanced aerospace composites both in ambient and harsh environmental conditions. We successfully correlate the amount of the encapsulated self-healing agent with the signal intensity and confirm non-destructively the quantity of the encapsulated self-healing agent mass for the first time in the literature using 1H NMR spin–spin relaxation techniques on urea–formaldehyde (UF) microcapsules of different diameters containing an epoxy healing agent. The amount of self-healing agent is shown to increase by reducing the capsule diameter; however, the reduced shell mass renders the capsules more fragile and prone to failure. Most notably, via NMR experiments conducted during thermal cycling simulating flight conditions, we demonstrate that the microcapsule integrity under thermal fatigue varies according to their size. Especially we experimentally verify that the microcapsules with the most sensitive shells are the 147 nm and 133 nm diameter microcapsules, which are the most commonly used in self-healing systems. Finally, we were able to retrieve the same results using a portable NMR spectrometer developed in-house for in situ microcapsule testing, thus demonstrating the potential of NMR relaxometry as a powerful non-destructive evaluation tool for the microcapsule production line.

Reciprocity-based closed-form solutions to guided waves in multilayered structures subjected to time-harmonic excitations

Ultrasonic guided waves provide an efficient tool for nondestructive evaluation and characterization of multilayered structures, e.g., of adhesively bonded joint in aerospace industry. In this article we investigate the propagation of guided waves in fully bonded multilayered plates excited by time-harmonic sources. By using the transfer matrix method, we propose explicit expressions of the free guided waves that depend on only one unknown constant representing amplitude. From these expressions, theoretical predictions of guided wave fields arising from a time-harmonic source are derived by using the reciprocity relations in elastodynamics. These very first closed-form solutions offer several distinct advantages, including efficient solution of inverse problems for materials characterization, direct calculation of guided waves at every point with a low computational cost and a benchmark to verify and improve numerical analysis of guided waves in multilayered structures. The obtained results are illustrated by computing guided wave motions in the bond region of an adhesively bonded lap joint, commonly used in automotive and aeronautical industries. The dispersion curves produced here are significant improvement upon those available in literature, as they are superimposed with the amplitude spectra values, enabling optimal selection of modes and frequencies for ultrasonic inspection. The analytical predictions of guided wave amplitudes in a three-layer adhesive joint model are numerically verified through finite element simulations, showing excellent agreement with the lowest guided wave modes.

Matrix cracking onset stress and strain as a function of temperature, and characterisation of damage modes in SiCf/SiC ceramic matrix composites via acoustic emission

The complex damage mechanisms that accumulate within SiC f /SiC ceramic matrix composites (CMCs) subject to thermal and mechanical stress are being investigated in anticipation of the material’s introduction into high performance gas turbine engines. Acoustic emission (AE) is recognised as a leading non-destructive evaluation (NDE) tool to this end, and was used in this study to determine the so-called matrix cracking onset stress under tensile load as a function of temperature up to a maximum of 1100°C. Onset stress was interpreted using three traditional measurements based on AE energy characteristics during monotonic tests to failure. Pattern recognition (PR) analysis was performed on the AE data, revealing a specific cluster of signals that correlated closely with the initial matrix cracking region of the stress-strain curve. Taken in isolation, the onset stress of this activity was significantly lower than the conventional value. PR results were investigated further, and isolated clusters were linked to damage modes anticipated at other specific regions of the stress history. A secondary series of experiments was performed on specimens representing the individual constituents of the CMC (single-phase SiC flexural bars, Hi-Nicalon™ fibre bundles and SiC f /SiC mini-composites) in attempts to further validate the corresponding AE signal characteristics. Matrix cracking and interphase debonding/sliding damage modes could be identified consistently, while fibre breaks remained difficult to isolate under the current experimental conditions.

Enhanced damage imaging in three-dimensional composite structures via electrical impedance tomography with mixed and level set regularization

Electrical impedance tomography (EIT) is a promising tool for nondestructive evaluation (NDE) of materials that exhibit stimulus-responsive electrical conductivity. To date, materials practitioners of EIT have used standard regularization methods such as smoothness-promoting operators to solve the ill-posed EIT inverse problem. However, more sophisticated and better performing regularization methods exist. It is essential that these other regularization methods be explored in order for EIT to see more widespread adoption in NDE. To that end, we present two novel regularization techniques – a mixed smoothness/focal method and a level set method – for application to damage imaging via EIT. These new techniques are experimentally validated on two three-dimensional composite components, a carbon black-modified glass fiber/epoxy tube and a carbon fiber/epoxy laminate airfoil subject to multiple damaging impacts. It is shown that both of the new regularization techniques markedly outperform traditional smoothness-only methods. These results are an important step towards adoption of more sophisticated EIT formulations in NDE and transition of EIT from the proof-of-concept phase and into practice for engineered materials.

Apex-shifted Radon transform for baseline-subtraction-free (BSF) damage scattered wave extraction

In ultrasonic structural health monitoring (SHM) and nondestructive evaluation (NDE), the scattered waves caused by damage sites and defects are the key to damage diagnosis. However, structural components and boundaries also interact with traveling waves, creating events that can bury damage scattered waves. The baseline subtraction method, which directly subtracts the waveform of a damage signal from that of a pristine baseline signal, is a common processing technique to separate these damage scattered waves. However, baseline subtraction is less effective when a component is measured in different environmental/loading conditions from when its baseline was recorded. For instance, baseline subtraction can be ineffective in aerospace structural parts because such parts expect significant and routine changes in ambient temperature, pressure, and humidity. To overcome the limitations of baseline subtraction, this paper proposes to develop an spex-shifted Radon transform (ASRT)-based damage scattered event extraction technique without baseline subtraction. Our proposed ASRT method converts the original time-space domain signals to a time delay–curvature–apex offset domain, which targets specific geometries of scattered/reflected waves in the domain and compresses them into a single point-like region in the new domain. In this domain, identifying and isolating targeted events becomes significantly easier. To benchmark the performance of this baseline-subtraction-free (BSF) method, ASRT is applied for signals acquired from (1) spectral finite element-based simulations to scan a water-immersed steel specimen (2) 3-D wave simulations in a bent aluminum plate, and (3) a full matrix capture for experimentally scanning a high-density polyethylene (HDPE) with multiple holes. The goal in each case is to target and separate events of interest from the original signals using the proposed algorithm. The results suggest the ASRT method is effective as a damage scattered wave extraction tool for ultrasonic SHM and NDE.

Pattern-recognizing-assisted detection of mildewed wheat by Dyes/Dyes-Cu-MOF paper-based colorimetric sensor array

In order to timely discriminate wheat with different mildew rates, a Dyes/Dyes-Cu-MOF paper-based colorimetric sensor array was designed. Using array points to capture volatile gases of wheat with different mildew rates, and output RGB values. The correlation between ΔR/ΔG/ΔB values and odor components was established. The ΔG values of array points 2′ and 3′ showed the best correlation with mildew rate, with R2 of 0.9816 and 0.9642. The ΔR value of 3 and the ΔG value of 2 correlate well with the mildew rate, with R2 of 0.9625 and 0.9502, respectively. Then, the ΔRGB values are subjected to pattern recognition processing, and LDA achieves 100% correct discrimination for all samples, or divides high and low mildew areas. This method provides an odor-based monitoring tool for fast, visual and nondestructive evaluation of food safety and quality through visualization of odors produced by different mildew rates.

Extraction of LIF features using sweep-frequency eddy current for conductivity and thickness evaluation of non-magnetic metallic plates

Sweep-frequency eddy current testing(ECT) is an efficient tool in nondestructive testing and evaluation due to its characteristics of non-contact, high sensitivity and abundant frequency information. In fact, the lift-off fluctuation is the main influencing factor to introduce the measurement errors. In this paper, the response signal feature, i.e. lift-off irrelevant frequency (LIF), has been found, which is immune to the effect of lift-off. Based on the characteristics, the sensor including two pairs of T-R coils is designed to obtain the feature point of LIF. Related analytical solutions and experiments are conducted to investigate the properties of LIF for non-magnetic materials, and the performance of LIF is also analyzed along with the conductivity and thickness of the tested piece. Hence, the LIF can provide the effective measurement of non-magnetic materials and immune to the lift-off fluctuation. The errors of thickness and conductivity measurement are 3.7% and 3.8% respectively.

Simultaneous determination of Young's modulus and Poisson's ratio in metals from a single surface using laser-generated Rayleigh and leaky surface acoustic waves

Material elastic moduli are used to assess stiffness, elastic response, strength, and residual life. Ultrasound (US) measurements of propagation wave speeds (for longitudinal and shear waves) are now primary tools for non-destructive evaluation (NDE) of elastic moduli. Most US techniques measure the time-of-flight of through-transmission signals or reflected signals from the back wall. In both cases, an independently determined sample thickness is required. However, US methods are difficult for complex (non-flat) samples. When the local thickness is unknown, the propagation speed cannot be determined. On the other hand, the propagation speed of Rayleigh waves can be calculated without knowledge of sample thickness, but another independent measurement is still required to compute both Young's modulus and Poisson's ratio. We present a comprehensive theoretical background, numerical simulations, and experimental results that clearly show that when the material density is assumed known, both elastic constants of an isotropic metal sample can be determined with laser-ultrasound by tracking two types of surface propagating waves without any sample contact (both signal excitation and detection are performed optically). In addition to a conventional surface, or Rayleigh, acoustic wave, a leaky surface wave can also be launched with nanosecond laser pulses in the thermoelastic regime of excitation (i.e., without material ablation) close to the source that propagates along the sample surface with speed close to that of bulk longitudinal waves. Samples can be of arbitrary shape and their thickness need not be measured.

Investigating the influence of smoothing approximations on analytical models of elastic waves in strongly scattering polycrystals

Ultrasonic scattering-based measurements are commonly used as sensitive tools for non-destructive evaluation (NDE) of metals. Existing analytical models can predict ultrasonic wavespeed and attenuation for statistically homogeneous metals exhibiting spatially dependent elastic constants. These models rely on two-point statistics that correspond to first-order smoothing approximation (FOSA) of the mass operator series present in the governing Dyson equation. The FOSA-based prediction agrees well with finite element (FE) results for a wide range of polycrystalline metals at ultrasonic frequencies in the stochastic regime. However, discrepancies become more pronounced with increasing single-crystal elastic anisotropy even at low frequencies in the Rayleigh limit. For example, a difference of 70% is present for Lithium. In this presentation, the next order or third-order smoothing approximation (TOSA) is introduced, and Rayleigh-limit attenuations and wavespeeds are derived analytically. In this context, the TOSA accounts for four-point correlation functions and, thus, a higher degree of multiple scattering effects are included. This presentation will focus on key points and assumptions pertaining to the derivation for results including the TOSA. The TOSA-based model improves predictions of longitudinal attenuation by more than 11% and 4% for polycrystalline Lithium or Nickel, respectively. Future extensions to higher frequencies and multiphase polycrystals will be described.

Laser-based finite element model reconstruction for structural mechanics

It is imperative to know the health condition of a structure during its service life. The development of laser scanning technology has created new opportunities to leverage high-resolution 3D laser scanning (3DLS) as a non-destructive evaluation tool for detailed geometrical information extracted for the creation of precise computational models. However, the workflow associated with this integration is indirect and presents challenges. The existing scan-to-model strategies use completely scanning data to generate a new finite element model (FEM), leading to excessive computational costs, especially if nonlinear analysis is required. In view of this, this study creates a pathway for a direct scan-to-model strategy suitable for translating condition data derived from a 3D laser scanning system into a FEM capable of describing the mechanical response of the component. Then, based on the scan-to-model strategy, a localized pathway to automatically identify the damaged parts and locally update the FEM is proposed. Instead of generating a new FEM of the damaged component, only the damaged parts are updated, which can reduce the computation cost. After that, the pathways were validated through laboratory-scale tensile testing using 3D Digital Image Correlation (3D-DIC), which enabled full-field deformation characterization and correlation with numerical model prediction. Results of this study provide the foundation of a computational framework for establishing the fundamental link between visually observable geometric and numerical models that engineers use to understand the performance of engineered systems.

Harnessing a direct scan-to-modeling approach for structural mechanics

To ensure the safety and reliability operation of infrastructures, accurate and rapid condition assessment of in-service infrastructures is extremely imperative. Image technologies and techniques, as a non-destructive evaluation (NDE) tool, have created new opportunities to achieve this. It is able to resolve sub-millimeter details including surface flaws and defects, providing a foundation for quantitatively linking observable features to operational performance. This linkage is possible when the quantified feature is directly integrated into tools suitable for describing mechanical response, such as the finite element method. However, the workflow associated with this integration is indirect and presents challenges. This work creates a pathway for a direct scan-to-model strategy suitable for translating condition data derived from a 3D laser scanning system into a computation model capable of describing the mechanical response of the component. The geometric characterization capabilities of the proposed approach and the influence of scan resolution on the geometric characterization are explored. Results of this study provide the foundation of a computational framework for establishing the fundamental link between visually observable geometric changes and the numerical models that engineers use to understand the performance of engineered systems.

Evaluating Log Stiffness Using Acoustic Velocity for Manufacturing Structural Oriented Strand Board

Oriented strand board (OSB) is an engineered panel product formed by layering strands of resinated wood in specific orientations into a mat, then pressing the mat at a high temperature to form a panel of desired strength and stiffness. OSB manufacturing facilities utilize small diameter logs from thinning operations and waste from harvesting. Considerable variation exists in the wood properties of the raw material and ideally the OSB industry would take advantage of such variation, however, it lacks the technology required to rapidly assess log quality on-site. Non-destructive evaluation (NDE) techniques based-on acoustics have the potential to rapidly segregate logs in the field, however the influence of acoustic-based log segregation on OSB panel properties is unknown. The aims of this project were to determine if log quality affects panel properties and if acoustic NDE technology is a satisfactory tool for determining log stiffness prior to entering the manufacturing process. It was found that low velocity (stiffness) logs produced panels with low stiffness while high and medium velocity (stiffness) logs produced panels with similar properties. The Director HM 200 was a satisfactory tool for determining log stiffness. Further studies are required to determine how to incorporate NDE tools into the manufacturing process.

Mechanical vibration modeling and characterization of a plastic-cased lithium-ion battery

Batteries often show the coupling change of multiple physical field characteristic parameters in the charging or discharging processes. Conventional battery modeling and characterization methods mainly focus on electrical or thermal parameters. Considering that battery state change can cause a change in the mechanical structure, research on the vibration characteristic modeling and characterization of a plastic-cased lithium-ion battery is carried out. By analyzing the mechanical structure of the battery, the first principles modeling method is selected to model the battery's mechanical performance. The vibration data in the process of battery charging and discharging are measured by a laser Doppler vibrometer (LDV). The obtained experimental data are used to identify the mechanical parameters of the battery. Based on the experimentael results, the root mean square error (RMSE) of the frequency domain amplitude fitting result of the model is less than 11.36%. The effectiveness of the battery mechanical vibration model is verified. The model and the characterization method provide tools for nondestructive battery state evaluation.