Nondestructive Evaluation Applications Research Articles

Quantum analogous spin states of ultrasonic guided waves

In quantum mechanics, spin is a physical property that dominates the topological behaviors. While manifesting the spin states they reveal complex interaction of physical parameters in a topological media. The guided waves’ inherent spin states are made of real physical spin angular momentum from the superposition of elastic waves. Thus, here the elastic spin state that naturally manifests by the ultrasonic guided waves in an elastic wave guide is explained through quantum analogous perspective. Guided wave modes are the superposition of two longitudinally polarized and two transverse polarized elastic wave potentials propagating in diverging and converging pattern. Spin nature of transverse waves is well known. Spin nature of longitudinal waves is also recently being explored. However, due to the unique modal superposition of guided Rayleigh-Lamb wave modes the physical understanding of spin state is incomplete for the guided waves in a bounded media. Unlike only one hybrid spin states described in earlier works, guided waves may manifest total six with four well defined hybrid spin states explicitly derived and explained in this article. These six spin states play crucial role in the physics of spin-momentum locking of guided waves. Two spin states originated from the interaction of similar potentials and four hybris spin states originated from the interaction of potentials with different directions of wave vector and polarization vector, as emerged in guided waves. Understanding from fundamentals and exploiting the phenomena of spin-momentum locking in guided waves may have several applications in nondestructive evaluation.

Pseudo-noise pulse-compression thermography: A powerful tool for time-domain thermography analysis

Pulse-compression is a correlation-based measurement technique successfully used in many nondestructive evaluation applications to increase the signal-to-noise ratio in the presence of huge noise, strong signal attenuation or when high excitation levels must be avoided. In thermography, the pulse-compression approach was firstly introduced in 2005 by Mulavesaala and co-workers [1], and then further developed by Mandelis and co-authors that applied to thermography the concept of the thermal-wave radar developed for photothermal measurements [2-3]. Since then, many measurement schemes and applications have been reported in the literature by several groups by using various heating sources, coded excitation signals, and processing algorithms. The variety of such techniques is known as pulse-compression thermography or thermal-wave radar imaging.Even despite the continuous improvement of these techniques during these years, the advantages of using a correlation-based approach in thermography are still not fully exploited and recognized by the community. This is because up to now the reconstructed thermograms' time sequences after pulse-compression were affected by the so-called sidelobes, i.e. the temperature time trends of the pixels exhibit oscillations, especially in the cooling stage, so that they do not reproduce the output of a standard thermography measurement. This is a severe drawback since it hampers an easy interpretation of the data and their comparison with other thermography techniques.To overcome this issue and unleash the full potential of the approach, this paper shows how it is possible to implement a pulse-compression thermography procedure capable of suppressing any sidelobe by using a pseudo-noise excitation and a proper processing algorithm.At the end of the procedure, time-sequences of thermograms are reconstructed that correspond to the sample response to a well-defined virtual excitation, namely a rectangular pulse, making the pulse-compression procedure “transparent”. This allows the analysis of pixel time trends by using thermal theory-driven processing such as thermal signal reconstruction, pulsed-phase thermography, etc. Moreover, by tuning the characteristic of the pseudo-noise excitation, it is possible to pass from simulating a very short excitation pulse, retrieving results analogous to pulsed-thermography, to simulating long-pulse excitation to match the sample spectral characteristics maximizing the signal-to-noise ratio. This makes the procedure very flexible and extremely attractive in many applications such as high-attenuating materials, characterization of fast thermal phenomena, and inspection of fragile samples inspection, e.g. paintings or other artworks, etc.

Anisotropic piezomagnetic behavior of wire and arc additively manufactured low carbon steel

The objective of this study is to investigate the piezomagnetic behavior corresponding to the mechanical properties of a low-carbon steel fabricated by wire arc additive manufacturing (WAAM) under tensile stress. WAAM rectangular tubes with a nominal thickness of 4 mm were fabricated with ER70S-6 wires using a continuous path with single way stacking between layers. Tests were carried out on WAAM steel specimens with three different orientations relative to the deposition direction extracted from rectangular tubes, and the evolutions of magnetic field around the specimens were recorded. The variation characteristics of piezomagnetic response at different loading stages were analyzed, highlighting the anisotropic nature of the piezomagnetic field evolution. The internal correlation between piezomagnetic field and tensile stress was explored. It is found that the piezomagnetic behavior of WAAM steel during the tensile process corresponds to the mechanical response. The Villari reversal points can be used to predict the yield strength and tensile ultimate strength of WAAM steel, and the area of the magnetic field-stress curve may be a measure of the ductility of WAAM steel. The theory of microscopic magnetic domains and the constitutive relation of ferromagnetic materials considering magnetocrystalline anisotropy were used to explain the experimental results. This study provides new insights into the anisotropic piezomagnetic properties of WAAM steel, offering potential applications in non-destructive evaluation of mechanical performance.

Performance Evaluation of Structural Health Monitoring System Applied to Full-Size Composite Wing Spar via Probability of Detection Techniques.

Probability of detection (POD) is an acknowledged mean of evaluation for many investigations aiming at detecting some specific property of a subject of interest. For instance, it has had many applications for Non-Destructive Evaluation (NDE), aimed at identifying defects within structural architectures, and can easily be used for structural health monitoring (SHM) systems, meant as a compact and more integrated evolution of the former technology. In this paper, a probability of detection analysis is performed to estimate the reliability of an SHM system, applied to a wing box composite spar for bonding line quality assessment. Such a system is based on distributed fiber optics deployed on the reference component at specific locations for detecting strains; the attained data are then processed by a proprietary algorithm whose capability was already tested and reported in previous works, even at full-scale level. A finite element (FE) model, previously validated by experimental results, is used to simulate the presence of damage areas, whose effect is to modify strain transfer between adjacent parts. Numerical data are used to verify the capability of the SHM system in revealing the presence of the modeled physical discontinuities with respect to a specific set of loads, running along the beam up to cover its complete extension. The POD is then estimated through the analysis of the collected data sets, wide enough to assess the global SHM system performance. The results of this study eventually aim at improving the current strategies adopted for SHM for bonding analysis by identifying the intimate behavior of the system assessed at the date. The activities herein reported have been carried out within the RESUME project.

Blood CO Status Classification Using UV-VIS Spectroscopy and PSO-optimized 1D-CNN Model

Rapid and effective blood carbon monoxide (CO) assessment is of great importance, especially in estimating CO-related morbidity and instituting effective preventive measures. The conventional detection methods using CO breath analysis lack sensitivity, while collecting biological fluid samples for CO level measurement is prone to external contamination and expensive for frequent use. This study proposes a one-dimensional convolutional neural network (1D-CNN) consisting of three stacked biconvolutional layers for binary classification of blood CO status using the diffuse reflectance spectroscopy technique. Iterative particle swarm optimization (PSO) has efficiently found the best network parameters to learn important features from the reflectance spectroscopy data. The findings showed good testing accuracy, specificity, and precision of 92.9%, 90%, and 89.7%, respectively, and a high sensitivity of 96.3% in determining abnormal blood CO among smokers using the proposed CNN network. Comparisons with eight existing machine learning and deep learning models revealed the proposed method’s effectiveness in classifying blood CO status while reducing computing time by 8–13 folds. The findings of this work provide new insights that are valuable for researchers in neural network design automation, healthcare management, and skin-related research, specifically for application in nondestructive evaluation and clinical decision-making.

A review of Electrical Resistivity Tomography (ERT) applications in non-destructive evaluation of construction materials

A review of Electrical Resistivity Tomography (ERT) applications in non-destructive evaluation of construction materials

Hadamard acoustic correlated imaging based on photoacoustic modulation with a single transducer

Conventional ultrasound technology based on spot scanning or phased array encounters significant challenge in real-time imaging with a single detector. In this paper, we present a Hadamard acoustic correlated imaging based on photoacoustic modulation with one transducer. The process of accurately generating the Hadamard acoustic field is to apply the carbon-nanotubes–polydimethylsiloxane composite to absorb the optimized Hadamard basis pattern. Taking advantage of correlated imaging, our system without scanning can reduce imaging artifacts and its resolution could be about four times higher than that of traditional ultrasound imaging. The use of a single transducer rather than an array of transducers can reduce the cost of the imaging system. Therefore, the proposed scheme can find applications in biomedical imaging and nondestructive evaluation.

Deep learning-assisted locating and sizing of a coating delamination using ultrasonic guided waves

This article proposes a deep learning-assisted nondestructive evaluation (NDE) technique for locating and sizing a coating delamination using ultrasonic guided waves. The proposed technique consists of sending a propagating guided wave into a coated plate with a transducer and measuring the corresponding time-domain signals by receivers at several locations at downstream distances from the source transducer. The received time-domain signals are then provided to a trained machine-learning (ML) algorithm, which subsequently outputs the location and size of any delamination flaws between the transducer and receivers. Numerical simulations show that the proposed NDE technique yields accurate results with high throughput, once the ML algorithm is well trained. Although training the ML algorithm is time-consuming, this training only needs to be done once for a given sample configuration. The results of this article demonstrate that the proposed technique has great potential for characterizing delamination flaws in practical NDE and structural health monitoring (SHM) applications.

Dynamic Defect Detection in Fast, Robust NDE Methods by Transfer Learning Based Optimally Binned Hypothesis Tests

ABSTRACT The structural integrity of safety-critical infrastructures diminishes over time, necessitating periodic inspections. The gathering of low-noise, precise nondestructive evaluation (NDE) readings for defect detection can be both time-consuming and costly. In practical applications, NDE data can be highly noisy due to factors like liftoff/stand-off distances, probe drift, scanning speed, and variations in data acquisition rates. Given the broad spectrum of potential uncertainties that can contribute to noise accumulation, characterizing the noise in such NDE data presents significant difficulties. As a result, the extraction of defect signals through deconvolution becomes challenging. This article introduces an NDE-based dynamic defect tracking framework designed for robust conditions. It incorporates regular periodic monitoring of the material under test (MUT) using a cost-effective, easy-to-implement magnetic flux leakage (MFL) probe. The framework proposes a dynamic setup that includes occasional, highly accurate, expensive MFL scans among regular, low-cost, noisy MFL scans. The objective is to detect and precisely track defect formation in metallic pipes over time, thereby enabling the efficient alarming and localization of defects before they reach detrimental sizes. A key characteristic of the proposed dynamic monitoring method is its noise type agnosticism in the low-cost MFL scans. It remains effective even when the underlying noise-producing uncertainties fluctuate significantly over time, a feature achieved through the use of transfer learning. The method transfers accurate information regarding the locations and sizes of existing corrosions from the detailed MFL scan to the subsequent noisy MFL inspections. With this supportive information from defective scan-points, it estimates the degradation of the signal-to-noise ratio (SNR) in the noisy MFL scans. The framework suggests binned hypothesis tests in noisy MFL scans, setting the level of aggregation based on the SNR estimate in the scan data. This proposed binned hypothesis test optimizes defect coverage and maintains control over the false discovery rate (FDR). Experimental MFL data, gathered under a wide range of uncertainties and defect types, illustrates the highly heterogeneous nature of noise distributions in low-cost MFL scans and the significant variance in SNR deteriorations. The necessity of using binned hypothesis tests in these low-cost MFL data is highlighted by the poor performance of pointwise multiple hypothesis tests. Finally, the high effectiveness of the proposed transfer learning-based binned hypothesis testing method is demonstrated. Although the method was applied to MFL data in this instance, it is also suitable for other NDE applications. The applicability of the algorithms has also been confirmed through validation on experimentally generated Eddy Current (EC) data.

Frequency sweep study on the generation of dual-mode second harmonics (DMSH) on an isotropic nonlinear elastic cylindrical rod by T(0,1) mode

Nonlinear ultrasonic (NLU) guided wave (GW) measurements are more sensitive to microscale defects than linear measurements. This nonlinear phenomenon is helpful for early-stage damage detection in material for nondestructive evaluation (NDE) and structural health monitoring (SHM) applications. The amplitude of the higher harmonics generated in the material serves as the basis for the NLU measurement. Recent studies have reported the presence of dual-mode second harmonic (DMSH) on an isotropic nonlinear elastic plate and cylindrical structures. The fundamental non-dispersive mode shear horizontal SH0 and torsional T(0,1) modes can generate simultaneously propagating dual-mode second harmonic(DMSH) on plate and cylindrical guided media respectively. For the case of cylinders, at phase matching condition two dominant second harmonic fundamental longitudinal (l(0,1)) and orthogonal torsional (t(0,1)┴) mode are generated with significant amplitude. The particle vibration of the t(0,1)┴ mode was present in both orthogonal directions compared to conventional T(0,1) mode and hence called orthogonal torsional mode. The present work aims to study the behaviour of DMSH at different frequencies through a frequency sweep study on a weakly nonlinear elastic cylinder of circular cross-section via numerical simulations and validated experimentally for some selected cases. The wave propagation of the T(0,1) mode at several selected frequencies from 300 kHz to 2.2 MHz is chosen to explore the second harmonic mode for better understanding. At frequencies below 1.25 MHz, l(0,1) mode is faster than t(0,1)┴ mode; above 1.25 MHz, it was the other way around. The behaviour of harmonics was observed to be in accordance with the group and phase velocities at the corresponding frequencies in the dispersion curves. The evidence for the presence of DMSH was validated experimentally for some selected frequency cases at different propagation distances. The significance of DMSH is explored via numerical simulations and found that t(0,1)┴ mode is sensitive towards material degradation, while all other generated wave modes were not affected. Research shows that enough energy is available in the generated DMSH to be noticed experimentally and in numerical simulations. This improved understanding of the generation of DMSH across different frequencies would be helpful in new advanced NLU-based NDE and SHM applications.

Deep-subwavelength ultrasonic imaging by MHz column-structured metalens: First evidence of quantitative visualization of subsurface defects

High-resolution ultrasonic imaging, which is highly demanded in nondestructive evaluation, is inherently limited by the detection wavelength. Acoustic metamaterial is an emerging technique to achieve subwavelength-resolution ultrasonic imaging beyond the diffraction limit due to its unprecedented acoustic properties. However, existing reports focus on metalenses for manipulating acoustic waves propagating in fluids like air and water, typically at a low-frequency range below 10 kHz. In this paper, a 0.5 MHz periodic column-structured metalens is designed and fabricated to realize deep-subwavelength ultrasonic imaging for quantitive visualization of subsurface defects in solid structures. The silicon-based metalens is designed based on Fabry–Pérot resonance theory. It consists of silicon columns arranged periodically with a lattice constant of 0.2 mm. The Fabry–Pérot resonance frequency is analyzed theoretically and the wave fields of the metalens at resonance mode are verified numerically. The subwavelength ultrasonic imaging performance of the proposed metalens is numerically proved and experimentally demonstrated. As a result, super-resolution ultrasonic imaging (λ/30, with λ being the wavelength) with a high resolving contrast is realized to identify two separated subsurface defects in a stainless-steel structure experimentally with the designed column-structured metalens. This work demonstrates a valuable deep-subwavelength imaging method that beyond traditional diffraction limits and paves the way for enhanced applications in nondestructive evaluation and biomedical diagnosis.

Scientometric Analysis of the Dynamics of Artificial Intelligence Applications in NonDestructive Testing and Structural Integrity Monitoring

This study aims to present a scientometric analysis of Artificial Intelligence (AI) applications in NonDestructive Testing and Evaluation (NDT&E) and Structural Integrity Monitoring. The data is collected from the research papers contained in the Web of Science Core Collection, covering studies on AI applications in various NDT methods employed across different industry sectors. The collected 654 research articles-dataset published between April 1989 and January 2023 was processed using CiteSpace software, which classified the dataset into twelve clusters. Moreover, a subset of the data pertaining to the relevant research in the nuclear industry was considered for analysis. Various metrics were used to analyse the consistency of the clusters and publications' influence and quality. The results, which quantify the dynamics and quality of research in AI for NDT&E, are given in visualised mappings, and tabulated data and the content of the major clusters was discussed to reveal the used AI and NDT&E methods and the sectors or industries where they have been used.

Frequency shifting of transmitted ultrasound in thick composites containing fiber wrinkles and its application in non-destructive evaluation

Thick composite structures are prone to defects such as fiber wrinkles and voids during manufacturing. It is challenging to accurately evaluate the forming quality of the structures using conventional ultrasonic inspection, due to the coupling effects between time-frequency features of ultrasound and mixed-type defects. Propagation behaviors of through-thickness transmitted ultrasound in thick composites with fiber wrinkles, voids and no defects were comparatively investigated by both simulation and experiment in this study. Influence of out-of-plane fiber wrinkles on the ultrasonic frequency shifting was studied by comparing the time-frequency characteristics of simulated ultrasonic signals after propagating different distances in the intact and wavy composites. Changes of transmission coefficients of converted transverse waves caused by fiber wrinkles were concluded be the reason for the appearance of high-frequency components above the excitation frequency in the transmitted ultrasound signal. Thereby ultrasonic defect inspection indices based on the phenomenon of ultrasonic frequency shifting were defined. Effects of interaction angles between ultrasonic propagation direction and fibers on the defined inspection indices was further investigated quantitatively. The thick composites with diverse defects were successfully diagnosed using the ultrasound frequency shifting and energy dissipation behaviors.

Industry 4.0 and NDE – AutosonicTM mini + Auto: Automatic system for periodical inspection and test of seamless aluminum-alloy gas cylinders (ISO 18119)

The Non Destructive Evaluation (NDE) is a fundamental process when high safety standards for the tested component are required. The evaluation may imply a combination of methods to achieve the highest Probability of Detection (POD) resulting in several data available which must be properly collected, processed, and stored for future reviews and for traceability reasons. All these requirements imply a sophisticated digital infrastructure and the usage of the most advanced Information Technology (IT) solutions to achieve computation speed, safe data processing and accessibility of the information. The Industry4.0 revolution is the result of the combination of digital technology to industrial processes for rethinking the performances in terms of automation, integration, crosslinking, availability and sharing of information. These principles can be applied in the NDE process as several products on the market are tested and monitored during the whole lifetime. The tracking of data, the secure data validation, and the need to avoid misuses and manipulations are new additional requirements for the NDE 4.0. Block chain technology, mainly known for crypto applications, is a promising technology for storing digital identity and test records offering traceability, safety and availability of the data. The present paper wants to present the Swiss Safety Center AG approach for a specific application case (retesting of gas cylinders according to ISO18119) where the guidelines and trends of NDE 4.0 have been successfully integrated in a fully automatic system, first in class for this application. The paper wants also to provides some insights about future trends and potential developments which may not be limited to this specific case but can be applied for other similar applications, e.g. in railways, manufacturing industry, automotive, aerospace and more in general in the NDE applications.

A Variational Formulation of Physics-Informed Neural Network for the Applications of Homogeneous and Heterogeneous Material Properties Identification

A new approach for solving computational mechanics problems using physics-informed neural networks (PINNs) is proposed. Variational forms of residuals for the governing equations of solid mechanics are utilized, and the residual is evaluated over the entire computational domain by employing domain decomposition and polynomials test functions. A parameter network is introduced and initial and boundary conditions, as well as data mismatch, are incorporated into a total loss function using a weighted summation. The accuracy of the model in solving forward problems of solid mechanics is demonstrated to be higher than that of the finite element method (FEM). Furthermore, homogeneous and heterogeneous material distributions can be effectively captured by the model using limited observations, such as strain components. This contribution is significant for potential applications in non-destructive evaluation, where obtaining detailed information about the material properties is difficult.

Quantile-Frequency Analysis and Deep Learning for Signal Classification

This paper proposes a new method for signal classification based on a combination of deep-learning (DL) image classifiers and recently introduced nonlinear spectral analysis technique called quantile-frequency analysis (QFA). The QFA method converts a one-dimensional signal into a two-dimensional representation of quantile periodograms (QPER) which represent the signal’s oscillatory behavior in the frequency domain at different quantiles. With a moving window, the QFA method can also covert a signal into a sequence of such two-dimensional representations, called short-time quantile periodograms, that are localized in time to represent the signal’s time-dependent or nonstationary properties. The DL image classifiers take these representations as input for signal classification. The benefit of this QFA-DL classification method in comparison with the traditional frequency-domain method based on the power spectrum and spectrogram is demonstrated by a numerical experiment using real-world ultrasound signals from a nondestructive evaluation application.

One-way collinear wave mixing in solids with cubic nonlinearity based on Murnaghan’s potential

Ultrasonic wave mixing is a powerful new nondestructive evaluation technique for accessing hidden subtle imperfections in materials. First, this paper derives the resonance conditions of one-way collinear mixing with cubic nonlinearity. The results show that the mixing of two collinear longitudinal waves can generate a resonant longitudinal wave, the mixing of two transverse waves can generate a resonant transverse wave, and the resonant longitudinal wave and transverse wave can be generated, respectively, when two primary longitudinal and transverse waves satisfy different resonance conditions. This is different from the case with quadratic nonlinearity. Furthermore, we obtain the analytical solutions of resonant waves generated by the mixing of harmonic longitudinal and transverse pulses. The waveforms are approximate hexagonal shapes according to the analysis of the envelopes. Finally, the numerical simulation results conducted on material aluminum prove the correctness of the analytical solution. Compared with quadratic nonlinearity, the resonant wave is more sensitive to material constants for some materials when considering one-way collinear mixing of primary longitudinal and transverse pulses based on cubic nonlinearity. The results provide new opportunities on mixing wave applications in nondestructive evaluation.

Nanoscale surface profile measurement using state space approach in digital holographic microscopy

Surface profile measurement at the nanoscale level has important applications in non-destructive testing and evaluation. The paper proposes a robust method for surface profilometry using digital holographic microscopy setup. The proposed method relies on extracting the phase map encoded in the hologram signal, which directly corresponds to the surface profile, using state space approach. The main advantage of the proposed method is high robustness against noise, which is demonstrated using numerical simulations. For designing the experimental system, a combination of Raspberry-Pi computer and camera module is used for hologram acquisition and processing, which is a step towards low cost imaging. For surface profile measurement, the experimental system has both temporal and spatial sensitivity parameters within 5 nanometers, which indicates robust design. In addition, experimental results show that the proposed method shows superior performance compared to the existing methods for measuring 100 nanometers surface profile features corresponding to different micro-structure regions of a standard calibration test target. Overall, the proposed method allows for single shot, non-contact and full-field measurement of nanoscale surface profile with additional benefits of noise robustness and low cost imaging design.

Combined Sensor for Capacitive Imaging and Size Measurement for Surface Features

Capacitive imaging (CI) has been successfully used in nondestructive evaluation (NDE) applications. Conventional capacitive electrodes applied to CI technology are generally planar, and only one capacitor type exists in one probe. This work proposes a combined capacitive sensor, which is mainly composed of triangular prism electrodes and auxiliary electrodes, and measurement system for CI technology. Triangular prism electrodes are designed to improve the two-dimensional (2-D) image resolution compared to those of planar electrodes. Two different spatial arrangements of driving and sensing electrodes are applied to achieve the 2-D imaging and depth detection of specimen features. The auxiliary electrode is developed to measure the sizes of surface features and distinguish surface and internal features. Double scans and image superimposition are employed to address image blurring and shape distortion in a single direction of the image due to the different imaging resolutions of probes in two perpendicular directions. The feasibility of the combined sensor in feature imaging and key parameter detection is verified through experiments. This work expands the functionality of conventional capacitive probes by combining different electrodes in one probe and lays a foundation for the subsequent analysis and further processing of CI technology.

Interpretable & Explainable Machine Learning for Ultrasonic Defect Sizing.

Despite its popularity in literature, there are few examples of machine learning (ML) being used for industrial nondestructive evaluation (NDE) applications. A significant barrier is the 'black box' nature of most ML algorithms. This paper aims to improve the interpretability and explainability of ML for ultrasonic NDE by presenting a novel dimensionality reduction method: Gaussian feature approximation (GFA). GFA involves fitting a 2D elliptical Gaussian function an ultrasonic image and storing the seven parameters that describe each Gaussian. These seven parameters can then be used as inputs to data analysis methods such as the defect sizing neural network presented in this paper. GFA is applied to ultrasonic defect sizing for inline pipe inspection as an example application. This approach is compared to sizing with the same neural network, and two other dimensionality reduction methods (the parameters of 6 dB drop boxes and principal component analysis), as well as a convolutional neural network applied to raw ultrasonic images. Of the dimensionality reduction methods tested, GFA features produce the closest sizing accuracy to sizing from the raw images, with only a 23% increase in RMSE, despite a 96.5% reduction in the dimensionality of the input data. Implementing ML with GFA is implicitly more interpretable than doing so with principal component analysis or raw images as inputs, and gives significantly more sizing accuracy than 6 dB drop boxes. Shapley additive explanations (SHAP) are used to calculate how each feature contributes to the prediction of an individual defect's length. Analysis of SHAP values demonstrates that the GFA-based neural network proposed displays many of the same relationships between defect indications and their predicted size as occur in traditional NDE sizing methods.