The ever-increasing demand for efficiency and cost improvements in lightweight structures with guaranteed safety and reliability is leading to the application of a damage-tolerant design philosophy. Here, accurate knowledge of structural health is critical to avoid catastrophic failures. This knowledge can be obtained by using advanced structural health monitoring (SHM) systems. For thin-walled lightweight structures, methods utilizing guided waves generated by piezoelectric transducers are well suited. The interaction between the guided waves and potential damages can be described by so-called wave damage interaction coefficients (WDICs). These WDICs are unique for each damage and depend solely on its characteristics for a given structure. Therefore, the comparison of known WDICs with estimated ones allows drawing conclusions about the current structural state. In this paper, a novel damage identification method for plate-like structures based on a database of such WDICs is presented. Selected damages are simulated numerically with finite elements to generate WDIC patterns. However, these simulations are computationally highly demanding, thus only a very limited number of damage scenarios can be simulated. This study proposes an innovative technique to substantially enhance the resulting WDIC database by using deep neural networks (DNNs). These DNNs enable smart interpolations and allow not only predicting WDICs for previously unseen damages at low computational costs but also the discovery of knowledge about the complex relationship between damage features and WDIC patterns. A comparison to other machine learning algorithms clearly shows the superior performance of the utilized DNNs for interpolating complex WDIC patterns. The proposed damage identification method is verified using advanced time-domain simulations of a large aluminum plate. A statistical analysis of correct identification rates in a common three-sensor setting is employed for assessing the general performance. It is demonstrated that carefully identified DNNs enable to accurately replicate and interpolate complex WDIC patterns. Furthermore, it is shown that these predicted WDICs allow identifying damage characteristics with high confidence.

This contribution investigates fatigue crack detection, localization and quantification in idealized necked double shear lugs using piezoelectric transducers attached to the lug shaft and analyzed by the electro-mechanical impedance (EMI) method. The considered idealized necked lug sample has a simplified geometry and does not includes the typical bearing. Numerical simulations with coupled-field finite element (FE) models are used to study the frequency response behavior of necked lugs. These numerical analyses include both pristine and cracked lug models. Through-cracks are located at 90${}^{\circ }$ and 145${}^{\circ }$ to the lug axis, which are critical spots for damage initiation. The results of FE simulations with a crack location at 90${}^{\circ }$ are validated with experiments using an impedance analyzer and a scanning laser Doppler vibrometer. For both experiments, the lug specimen is excited and measured using a piezoelectric active wafer sensor in a frequency range of 1 kHz to 100 kHz. The dynamic response of both numerical calculations and experimental measurements show good agreement. To identify (i.e., detect, locate, and quantify) cracks in necked lugs a two-step analysis is performed. In the first step, a crack is detected data-based by calculating damage metrics between pristine and damaged state frequency spectra and comparing the resulting values to a pre-defined threshold. In the second step the location and size of the detected crack is identified by evaluation of specific resonance frequency shifts of the necked lug. Both the search for frequencies sensitive to through-cracks that allow a distinction between the two critical locations and the evaluation of the crack size are model-based. This two-step analysis based on the EMI method is demonstrated experimentally at the considered idealized necked lug, and thus, represents a promising way to reliably detect, locate and quantify fatigue cracks at critical locations of real necked double shear lugs.

The present paper comprehensively investigates the complex interaction between ultrasonic guided waves and local structural discontinuities, such as damages, through highly sensitive features: so-called wave damage interaction coefficients (WDICs). These WDICs are unique for each structural discontinuity and depend solely on their characteristics for a given structure and condition. Thus, they can be particularly useful for advanced assessment of lightweight structures in the context of non-destructive evaluation and structural health monitoring. However, the practical application of WDICs entails significant difficulties due to their sensitivity and complex patterns. Therefore, this study attempts to guide researchers and practitioners in the estimation of WDICs from numerical simulations and physical experiments. Detailed investigations are made for an aluminum host plate modified by artificial structural discontinuities, i.e., surface-bonded steel sheets. The numerical simulations are performed to predict WDICs and study sensitivities using a sophisticated finite element model. The experimental setup uses piezoelectric transducers to excite guided waves in the host plate. A single scanning laser Doppler vibrometer measures the scattered guided waves caused by the surface-bonded steel sheets, and the resulting WDICs with possible influences are investigated. In both cases, the orientation and thickness of the attached steel sheets were varied to create 12 different damage scenarios. In general, the comparison between numerical and experimental WDICs show good agreement. This underpins the applicability of the general methodology for simulating and measuring WDICs over all scenarios. Furthermore, the WDIC scattering patterns reveal a clear dependency of the peaks in the back-scattered reflections for both the numerical and experimental amplitude coefficients on the damage orientation, basically following the law of reflection. However, some discrepancies between both studies were observed. Numerical sensitivity analysis identified the adhesive layer as one reason for such differences. Additionally, misalignment errors in the experimental measurements were also found to affect WDICs. Therefore, an improved baseline subtraction method is proposed, which clearly enhances the experimental WDICs. Finally, an experimental sensitivity study of WDICs for selected sensing radii revealed only a minor influence. All these investigations were made for the amplitude as well as the phase representation of WDICs. Thus, these findings may open the way to future research and development of techniques employing WDICs for advanced applications of non-destructive evaluation and structural health monitoring.

Thin-walled structures are widely used in aeronautical and aerospace engineering due to their light weight and high structural performance. Ensuring their integrity is crucial for safety and reliability, which is why structural health monitoring (SHM) methods, such as guided wave-based techniques, have been developed to detect and characterize damage in such components. This study presents a novel damage identification procedure for guided wave-based SHM using deep neural networks (DNNs) trained with experimental data. This technique employs the so-called wave damage interaction coefficients (WDICs) as highly sensitive damage features that describe the unique scattering pattern around possible damage. The DNNs learn intricate relationships between damage characteristics, e.g., size or orientation, and corresponding WDIC patterns from only a limited number of damage cases. An experimental training data set is used, where the WDICs of a selected damage type are extracted from measurements using a scanning laser Doppler vibrometer. Surface-bonded artificial damages are selected herein for demonstration purposes. It is demonstrated that smart DNN interpolations can replicate WDIC patterns even when trained on noisy measurement data, and their generalization capabilities allow for precise predictions for damages with arbitrary properties within the range of trained damage characteristics. These WDIC predictions are readily available, i.e., ad hoc, and can be compared to measurement data from an unknown damage for damage characterization. Furthermore, the fully trained DNN allows for predicting WDICs specifically for the sensing angles requested during inspection. Additionally, an anglewise principal component analysis is proposed to efficiently reduce the feature dimensionality on average by more than $90\%$ while accounting for the angular dependencies of the WDICs. The proposed damage identification methodology is investigated under challenging conditions using experimental data from only three sensors of a damage case not contained in the training data sets. Detailed statistical analyses indicate excellent performance and high recognition accuracy for this experimental data-based approach. This study also analyzes differences between simulated and experimental WDIC patterns. Therefore, an existing DNN trained on simulated data is also employed. The differences between the simulations and experiments affect the identification performance, and the resulting limitations of the simulation-based approach are clearly explained. This highlights the potential of the proposed experimental data-based DNN methodology for practical applications of guided wave-based SHM.

Reliable and precise damage localization in mechanical structures is of high importance in the context of structural health monitoring (SHM). The acoustic emission (AE) method has already shown its excellent suitability for damage localization. However, low signal-to-noise ratios (SNRs) are often prevalent in SHM, thus an increase in localization accuracy and robustness is still in demand. The present study faces this task through the integration of various model knowledge for AE source localization. The basis of the presented algorithm is the consideration of the dispersive behavior of elastic waves in thin-walled structures. The continuous wavelet transform (CWT) is used to obtain time-frequency representations of the signals, where frequency-dependent values for time-of-arrival (TOA) are extracted. Furthermore, the algorithm incorporates the knowledge that all sensors receive signals with the same time and location of origin, as well as the slightly different sensitivity of the theoretically equal sensors. The final localization results are achieved by a two parameter grid search optimization. The algorithm is experimentally tested on a large aluminum plate with four piezoelectric wafer active sensors (PWASs) arranged in an array of 100 mm × 100 mm. The mean localization error of pencil lead breaks at ten different positions within the sensor array is used as an accuracy measure. It is shown that as more of the described model knowledge is incorporated into the localization, the accuracy increases. With the final algorithm, the mean localization error is more than halved compared to AE localization based on classical TOA estimation. Although the experiment described is conducted under laboratory conditions, the remarkable increase in accuracy suggests that AE source localization may be successful even at low SNR as typical for operational conditions.

In this paper, recent advancements in the development of a guided wave-based damage identification approach using wave damage interaction coefficients (WDICs) and deep neural networks (DNNs) are presented. These WDICs uniquely describe the complex scattering of guided waves around possible damages and depend on the properties of the damage itself. Hence, they are utilized as physics-based and highly sensitive damage features herein. It is demonstrated, that DNNs can effectively learn intricate relationships between damage characteristics and complex-shaped WDIC patterns from a compact sized training dataset. In this study, two training datasets are created by numerical finite element simulations and experimental scanning laser Doppler vibrometer measurements using a pseudo-damage approach. Therefore, the orientation and thickness of surface-bonded artificial damages are varied to generate the training data of 12 selected damage scenarios. The generalization capabilities of the fully trained DNNs allow to accurately predict WDICs even for damage scenarios unseen during training. The presented damage identification method leverages this powerful ability to characterize properties of unknown damages. Once trained, the accurate DNN predictions become available promptly and can be compared with measured WDICs from an unknown damage for selected sensor positions. The performance of both simulation-based and experiment-based structural health monitoring approaches are assessed, while also addressing current limitations and possible enhancements. For example, the great potential of incorporating the phase information of the complex-valued WDICs in the identification procedure is discussed. Hence, this study highlights the latest advancements in the development of the presented damage identification method with promising results and provides valuable insights in the application of WDICs as physics-based features for DNNs.