Computational efficient methods for the uncertainty quantification of eddy current testing problems and their practical applications

Metal surfaces on industrial equipment are susceptible to fracture when subjected to extreme pressure and speed conditions. The safety of the parts is at risk and their service life is decreased by these fractures. One of the primary difficulties in developing eddy current non-destructive testing (NDT) sensors is locating fractures in any direction. The limitation is that fractures that are not perpendicular to the current flows produced cannot be detected by eddy current-based approaches. To locate arbitrary orientation fractures in conductive non-ferrous materials, this work explores the use of a rotating electromagnetic field technique and provides a novel rotating uniform eddy current (RUEC) system. This novel approach has greatly improved the detection of fractures in any orientation. The impedance signature of the fracture is investigated using a three-dimensional finite element (FE) simulation model of the new RUEC system. The rotating alternating current field measurement (RACFM) approach, which was designed to detect artificial cracks at any angle in underwater structures, is used in[1] to validate the model proposed in this study. The efficacy of the RUEC system and its potential in the detection of different fracture orientations in the aluminium specimen are demonstrated by the simulation results.

In this study, we analyzed transverse cracks in rails using eddy current testing. Quantitative analysis was performed on transverse crack defect signals ascertained by actual flaw detection and finite element simulation of the rail that had developed a central transverse crack. The conductivity and width of the finite element model were equivalent to those of the actual rail. By analyzing the distribution of eddy current on the rail surface, the relationship between the variation in the density of eddy current and size of transverse crack was obtained. Experimental and simulation results indicated that the application of eddy current testing in quantitative analysis of a rail flaw was feasible and would be a valuable reference in future research.

The accuracy of modal parameter estimates from estimation methods built in the framework of experimental modal analysis (EMA) can be assessed by several methods provided the information of input loadings and output responses. However, a deeper investigation is necessary for estimation methods built in the operational modal analysis (OMA) framework to establish confidence boundaries for the modal parameter estimates. This paper aims to estimate uncertainties of the modal parameter estimates by testing the sensitivity of the damped natural frequencies, damping ratios, and mode shapes to the choice of the estimation method and data acquisition settings used in this method. The uncertainty estimates of the modal parameter estimates are tested for changes in the boundary conditions. The tests provide insights into tendencies for the accuracy of the modal parameter estimates when the boundary conditions provide a different set of “true” modal parameter values. A simple cantilever beam experimental setup is used to obtain benchmark modal parameter estimates from EMA that are used to estimate the accuracy of the modal parameter estimates from OMA. The method’s robustness in estimating uncertainties and accuracies for modal parameter estimates is tested for several independent experiments. The boundary conditions for the cantilever beam are changed to test the influence of altering modal parameter estimates on the estimated uncertainties and accuracies. The boundary conditions are changed using materials with different elastic properties and the connection pressure between the clamping device and beam. A method presented in Paulsen et al. (Proceedings of the 9th International Operational Modal Analysis Conference, IOMAC, 2022) calculates a representative modal parameter estimate from a set of modal parameter estimates based on weightings obtained from the modal assurance criterion. The method’s ability to reduce uncertainties and increase accuracies of the representative estimate is demonstrated by repeating a test setup ten times. The results present simultaneously a reduction of uncertainties and an increase of accuracies for the representative modal parameter when the weighting method is used. An evaluation of dependencies between the estimated uncertainties and accuracies finds a proportional relation for the damped natural frequency when the uncertainties are described as a relative standard deviation. The analysis presents higher accuracy for the damped natural frequency and mode shape estimates compared to the damping factor, and the accuracy of the damping factor is dependent on the actual value of the damping factor. These phenomena for accuracy are well known and indicate that the uncertainties of modal parameter estimates can be assessed through a sensitivity test of estimation methods and data acquisition parameters.

This paper presents focus on physical feature extraction and parameter estimation for satellites in space. In the context of increasingly prominent space security issues, it is necessary to improve the security and protection capabilities of the space system, especially the refined feature extraction and recognition technology of space targets. However, the feature extraction methods based on optical or radar imagery are limited by resolution and observation conditions, making it difficult to extract refined features. This paper is based on the attribute scattering center theory, using high-frequency electromagnetic wave detection method. Through the attribute parameter estimation result of the scattering center, the scattering structure on the space target can be identified and its distribution position can be analyzed, and the structure and size of the typical parts in the space target can be extracted. Aiming at the problem of high parameter dimension and large amount of calculation, an attributed scattering centers parameter estimation method with amplitude and phase separation is proposed, which reduces the time complexity of parameter estimation by an order of magnitude, saves system resources and increases the parameter estimation rate, and the estimation accuracy is better than 90%. In terms of the efficiency and accuracy of parameter estimation from simulation and experimental data, the effectiveness of the proposed method in this paper is verified.

The estimation of sinewave parameters has many practical applications in test and data processing systems. Measuring the effective bits of an analog-to-digital converter and linear circuit identification are some typical examples. If a sinew ave's frequency is known, there is an established linear method to estimate the other parameters. But when none of the parameters are known (which is usually the case in practical situations), the estimation problem becomes more difficult. Traditional approaches to this task applied an iterative, sinewave curve-fit algorithm. Two problems with this technique are that convergence is often slow and not always guaranteed and the results of different trials may be inconsistent due to trapping at a local minimum. Recently, a non-iterative algorithm has been developed which computes all four sine wave parameters directly. The algorithm combines a nonlinear technique and windowing to compute the estimates. Although this method is faster and more consistent than the curve-fit approach, one disadvantage is that the accuracy of some estimates tends to deteriorate rapidly if the sinusoid is corrupted by a high level of noise distortion. This study presents an improved algorithm to extract the four parameters of an unknown sinusoid from a sampled data record even though the samples may be distorted by a high level of noise. Given this record, the proposed method first computes the FFT (Fast Fourier Transform) of the data. Analysis of the resulting frequency spectrum provides a rough estimate of the sinewave's fundamental frequency. Next, a bandpass filter designed around this frequency is used to eliminate much of the noise from the samples. Applying the existing four-parameter estimation algorithm to the filtered data, yields a more accurate frequency estimate. Finally, this new value, together with the original (noisy) data record is input to the three-parameter estimation algorithm to determine the remaining sinewave parameters. Simulation results indicate this proposed (new) algorithm not only shows substantial improvement in the accuracy of parameter estimates, but also produces consistent results for higher levels of noise distortion than previous methods have achieved.

In traditional eddy current testing, crack orientation and direction of the eddy current are closely related. This becomes particularly problematic when cracks are oriented at specific angles, as the fixed transmitter–receiver mode creates an eddy current field that often results in signal blind spots, thereby reducing detection performance. To address this issue, this paper proposes a time-division multiplexing (TDM)-based multi-mode eddy current testing (ECT) method specifically designed for detecting directional defects in metallic materials. By combining multiple excitation modes, this approach gathers more comprehensive multi-angle, multi-frequency, multi-frequency and multi-mode information, which strengthens directional-crack detectability and improves accuracy and reliability. The study compares the variation in induced voltage amplitudes under single and mixed excitation conditions, then their correlation with various directional defects is analysed. Finite element simulations are used to evaluate the impact of key parameters such as coil excitation frequency, centre-to-centre distance and outer radius on detection sensitivity as well. Subsequently, the effects of defect length, width, depth and orientation on the induced voltage signal are investigated. Finally, an experimental platform based on time-division multiplexing is constructed to thoroughly validate the method with various directional defects in metal components.

The study discusses a proper numerical modeling of stress corrosion crack (SCC) in finite element simulations, mainly from the viewpoint of the distribution of conductivity along the surface of crack. Two SCCs introduced into austenitic stainless steel plates are studied. SCCs are modeled as a region with a constant width, and non-uniform conductivity along surface of crack in the direction of depth of the SCCs, on the basis of the true profile revealed by destructive tests. Eddy current signals gathered by a differential probe with several frequencies are analyzed. The results show that a more appropriate model of SCC can be obtained by considering non-uniform conductivity.

Study on the Optimization of Eddy Current Testing Coil and the Defect Detection Sensitivity

Proton Exchange Membrane (PEM) fuel cells represent a promising clean energy technology due to their high efficiency, environmental sustainability, and wide applicability in transportation and stationary power systems. Accurate parameter extraction from PEM fuel cell models is critical for reliable performance prediction, control, and optimization. However, this task is challenging because of the nonlinear, multimodal, and highly coupled characteristics of fuel cell models. To address this challenge, this paper proposes an Enhanced Elk Herd Optimizer (EEHO), incorporating a novel best-bull–guided differential reproduction mechanism to improve search accuracy, convergence speed, and robustness. The proposed enhancement enables a portion of offspring solutions to be generated by perturbing the global best solution using scaled differences between randomly selected herd members. This mechanism strengthens exploitation around promising regions while maintaining population diversity and preventing premature convergence. The EEHO is applied to extract seven unknown parameters of PEM fuel cell models by minimizing the sum of squared errors between experimental and simulated voltage data. The effectiveness of the proposed method is validated using two commercial PEM fuel cell stacks, namely a 250 W stack and a BCS 500 W stack. Extensive comparative evaluations against the conventional Elk Herd Optimizer and several well-established methods demonstrate that the EEHO achieves superior performance in terms of accuracy, convergence speed, robustness, and statistical consistency. The proposed algorithm attains lower error values, faster convergence, and more stable performance across multiple independent runs. Furthermore, the extracted parameters produce highly accurate voltage and power characteristics, closely matching experimental observations. The results confirm that the proposed EEHO provides an efficient, reliable, and robust optimization framework for PEM fuel cell parameter extraction and offers strong potential for broader applications in energy system modeling, intelligent optimization, and renewable energy optimization problems. Quantitatively, the proposed EEHO achieved a significant reduction in the averages of the Sum of Squared Errors (SSE) of up to 24.96% and 23.29% compared with the conventional EHO for the 250 W stack and a BCS 500 W stack, respectively, demonstrating its superior accuracy in parameter estimation. To further validate the robustness and generalization capability of the proposed EEHO, two additional commercial PEM fuel cell datasets, of Ballard Mark V and Modular SR-12, are investigated and compared against several state-of-the-art optimization algorithms. The results, supported by Wilcoxon and Friedman statistical tests and boxplot analyses, confirm that EEHO consistently achieves superior accuracy, stability, and convergence reliability across different operating conditions.

Acceptability of inversely-modelled parameters for non-equilibrium sorption of pesticides in soil

The sensitivity of marginal maximum likelihood es timation of item and ability (θ) parameters was ex amined when the prior θ distributions are not matched to the underlying θ distributions. Thirty sets of 45-item test data were generated by specifi cation of three types of underlying θ distributions. They were then analyzed with PC-BILOG. Appropri ate specification of the prior θ distribution increased the accuracy of estimation for item and θ param eters when the sample size was large. With a small dataset, the appropriate specification of the prior increased the accuracy of θ parameter estimation, but it did not have that effect on item parameter esti mation. Only with a large dataset and matched under lying and prior θ distributions did increasing the number of quadrature points improve the accuracy of estimation of the item parameters. However, the ac curacy of θ estimation was increased by increasing the number of quadrature points, regardless of sample size and appropriateness of the prior θ distribution. The number of examinees had an im portant effect on the accuracy of item parameter estimation.

During fast point-to-point motion, the inherent joint flexibility could be detrimental in terms of residual vibration. Aiming to minimize the vibration, the command shaping method has been developed so as to remove critical energy from the input profile at resonant frequencies. Since this method requires information of a physical model in order to find the target frequencies, the quality of the shaped command profile relies on the accuracy of the model parameter estimation. Therefore, in this work, a system identification method using Instrumental Variables is applied from the literature. Compared with the classic Ordinary Least Square method, the IV approach has successfully improved the estimation of parameters, based on simulation results. The accuracy of parameter estimation influences the command profile, as does the feedback controller. In this work, starting from a mathematical derivation with a mismatch model due to a feedback controller called Computed Torque Control, insight for the closed-loop system is given with regard to the interaction between control gains and the actual resonant frequencies. It is found that the control gain is able to modify the actual resonant frequency curve, and push it into or out of the shaping bounds which are generated from the command shaping method. Further analysis based on the simulation results shows that the overlap area between the shaping bounds and the actual frequencies affects the level of residual vibration. In light of this fact, an optimal control gain exists and is found when the estimation error is in a certain range. At the end, recommendations for choosing the control gains are provided.

ABSTRACTImpulsive noise exists widely in ocean environment and statistical parameters of impulsive noise are necessary for ocean signal processing and communication system. However, statistical parameters are generally assumed known or acquired through complicated calculations. In this letter, a hybrid deep neural network based parameter estimation is proposed for ocean impulsive noise. The proposed method formulates the parameter estimation as a non‐linear mapping problem to be solved by deep learning network. The network incorporates one dimensional convolutional neural network to extend noise signals into new feature space without destroying large‐amplitude characteristics. Then the refined features are input to stacked long‐short term memory modules for temporal feature exploration considering temporal correlations inherently in sequential noise signals and the parameters are output through fully connected layers. The proposed network is verified and analysed through impulsive noise datasets from acknowledged ocean impulsive models and real‐test ocean noise. Experimental results prove the advantages of proposed method in parameter estimation accuracy.

Semi-analytical solution of eddy current testing problem is presented in the paper. An excitation air-core coil is located above a conducting plate with two flaws in the form of cylindrical holes located at top and bottom parts of the plate. The change in impedance of the coil is computed for different frequencies of the excitation current. Potential applications (analysis of the effect of corrosion, estimation of thickness and conductivity of metal coatings and quality testing of spot welding) are discussed.

Comparison of Fourier and Bayesian analysis of nmr signals. I. Well-separated resonances (the single-frequency case)