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As the most popular mechanism, the generalized Snell's law has been applied extensively to design metasurfaces for wave manipulation. By modulating phase profile using metasurfaces, various novel wave transformations have been demonstrated. However, it has been found that the performance of these metasurfaces cannot be fully determined by the generalized Snell's law and in some cases, the wave fields appear to be contradictory to what predicted by the generalized Snell's law. In this work, a systematic numerical study is conducted to investigate the generalized Snell's law for elastic waves. The inherent assumptions of the generalized Snell's law are examined first followed by the study of the effects of various implementation issues on the performance of the metasurfaces. In particular, the fundamental mechanism for producing wave components that do not obey the generalized Snell's lay is identified and theoretically justified. Design guidelines for metasurfaces for improved performance are provided.

Data-driven methods have emerged as promising approaches for guided wave-based damage localization. The success of the methods highly depends on the amount and the quality of the training data. Modeling training data are easy to obtain and abundant but could be unrealistic with biased model parameters and experimental uncertainties unconsidered. Experimental training data are realistic but scanty due to the high cost and low accessibility. To tackle this problem, this work utilizes both types of data to collect sufficient training data and learn a mapping function invariant to the modeling errors and experimental noises in a supervised manner, and thus to improve localization accuracy. Specifically, deep metric learning is conducted on the hybrid data to identify a distance metric, based on which the discrepancy between two sets of data is minimized, i.e., the distance metric is insensitive to the superfluous variations caused by modeling errors and experimental noises. Then, a representative non-parametric regression algorithm that relies on the distance metric, kernel regression, is used to predict damage locations. The performance of the proposed method is demonstrated on damage localization in plates and compared with several other data-driven methods. Results show that that proposed method can serve as a general strategy to overcome the shortage of labelled training data in data-driven methods for damage localization.

Various metasurfaces have been designed based on the generalized Snell’s law (GSL), but their performances are undermined by extra propagating waves that do not follow the GSL, especially when the phase gradient is large [1]. Although a modified version of GSL has been proposed for acoustic metasurfaces to describe the extra waves [2], the underlying mechanism of extra wave generation remains unclear. For elastic metasurfaces, such extra waves also exist as shown in Figure 1, indicating that the GSL might be invalid under some circumstances. In light of this, a systematic numerical study on the GSL for elastic waves is performed. It is found that mismatched impedance, material discontinuity, and phase discontinuity are the sources of the extra waves. The generation mechanisms of the extra waves from these sources are identified and theoretically justified. Based on these results, a guideline on metasurface design for improved performance is devised.

Data-driven methods have emerged as promising approaches for guided wave-based damage localization. The success of the methods highly depends on the amount and the quality of the training data. Modeling training data are easy to obtain and abundant but could be unrealistic with biased model parameters and experimental uncertainties unconsidered. Experimental training data are realistic but scanty due to the high cost and low accessibility. To tackle this problem, this work utilizes both types of data to collect sufficient training data and learn a mapping function invariant to the modeling errors and experimental noises in a supervised manner, and thus to improve localization accuracy. Specifically, deep metric learning is conducted on the hybrid data to identify a distance metric, based on which the discrepancy between two sets of data is minimized, i.e., the distance metric is insensitive to the superfluous variations caused by modeling errors and experimental noises. Then, a representative non-parametric regression algorithm that relies on the distance metric, kernel regression, is used to predict damage locations. The performance of the proposed method is demonstrated on damage localization in plates and compared with several other data-driven methods. Results show that that proposed method can serve as a general strategy to overcome the shortage of labelled training data in data-driven methods for damage localization.

Various metasurfaces have been designed based on the generalized Snell’s law (GSL), but their performances are undermined by extra propagating waves that do not follow the GSL, especially when the phase gradient is large [1]. Although a modified version of GSL has been proposed for acoustic metasurfaces to describe the extra waves [2], the underlying mechanism of extra wave generation remains unclear. For elastic metasurfaces, such extra waves also exist as shown in Figure 1, indicating that the GSL might be invalid under some circumstances. In light of this, a systematic numerical study on the GSL for elastic waves is performed. It is found that mismatched impedance, material discontinuity, and phase discontinuity are the sources of the extra waves. The generation mechanisms of the extra waves from these sources are identified and theoretically justified. Based on these results, a guideline on metasurface design for improved performance is devised.

Lamb wave-based SHM technology for damage detection and localization in plate-like structures has typically relied on post-processing of ultrasonic guided waves. Traditionally, the damage localization is realized using the time-of-flight (TOF) of damage-scattered waves. However, this method often requires the identification of a pure mode from the wave signal which is difficult in many cases. Damage index (DI) based methods offer another type of approaches that do not need such singal explanation. Since DI alone doesn't contain temporal information, data fusion of signals from multiple actuator-sensor pairs must be performed for localization. As a result, a relatively dense actuator-sensor network is needed, and localization can only be realized within the region covered by the network. Realizing that temporal information contained in the wave signal is extremely important to damage localization, we propose a time-varying DI feature that preserves the temporal information to improve localization accuracy. In addition, we propose to use one-dimensional convolutional neural network (1-D CNN) to correlate the time-varying DI directly with the damage location. The equivariance property of CNN preserves the temporal information. The efficiency and feature extraction capability of the CNN help to build a neural network model with certain generalization capability, and thus the model trained on one plate can be applicable to a new plate. The performance of the proposed method was demonstrated in three cases: localization in the same plate with different damage locations, localization in a new plate with the same damage locations, and localization in a new plate but with different damage locations. Despite that only four transducers were used, and limited experimental data for training were available, good results have been obtained. Performance comparison with several other existing methods was also conducted.

Lamb wave-based SHM technology for damage detection and localization in plate-like structures has typically relied on post-processing of ultrasonic guided waves. Traditionally, the damage localization is realized using the time-of-flight (TOF) of damage-scattered waves. However, this method often requires the identification of a pure mode from the wave signal which is difficult in many cases. Damage index (DI) based methods offer another type of approaches that do not need such singal explanation. Since DI alone doesn't contain temporal information, data fusion of signals from multiple actuator-sensor pairs must be performed for localization. As a result, a relatively dense actuator-sensor network is needed, and localization can only be realized within the region covered by the network. Realizing that temporal information contained in the wave signal is extremely important to damage localization, we propose a time-varying DI feature that preserves the temporal information to improve localization accuracy. In addition, we propose to use one-dimensional convolutional neural network (1-D CNN) to correlate the time-varying DI directly with the damage location. The equivariance property of CNN preserves the temporal information. The efficiency and feature extraction capability of the CNN help to build a neural network model with certain generalization capability, and thus the model trained on one plate can be applicable to a new plate. The performance of the proposed method was demonstrated in three cases: localization in the same plate with different damage locations, localization in a new plate with the same damage locations, and localization in a new plate but with different damage locations. Despite that only four transducers were used, and limited experimental data for training were available, good results have been obtained. Performance comparison with several other existing methods was also conducted.

Lamb wave-based SHM technology for damage detection and localization in plate-like structures has typically relied on post-processing of ultrasonic guided waves. Traditionally, the damage localization is realized using the time-of-flight (TOF) of damage-scattered waves. However, this method often requires the identification of a pure mode from the wave signal which is difficult in many cases. Damage index (DI) based methods offer another type of approaches that do not need such singal explanation. Since DI alone doesn't contain temporal information, data fusion of signals from multiple actuator-sensor pairs must be performed for localization. As a result, a relatively dense actuator-sensor network is needed, and localization can only be realized within the region covered by the network. Realizing that temporal information contained in the wave signal is extremely important to damage localization, we propose a time-varying DI feature that preserves the temporal information to improve localization accuracy. In addition, we propose to use one-dimensional convolutional neural network (1-D CNN) to correlate the time-varying DI directly with the damage location. The equivariance property of CNN preserves the temporal information. The efficiency and feature extraction capability of the CNN help to build a neural network model with certain generalization capability, and thus the model trained on one plate can be applicable to a new plate. The performance of the proposed method was demonstrated in three cases: localization in the same plate with different damage locations, localization in a new plate with the same damage locations, and localization in a new plate but with different damage locations. Despite that only four transducers were used, and limited experimental data for training were available, good results have been obtained. Performance comparison with several other existing methods was also conducted.

In structural health monitoring or development of an ultrasonic touchscreen, one often needs to localize a Lamb wave scatterer. That is, to identify the position of an object that perturbs the field of Lamb waves. However, the applicability and the effectiveness of the existing localization algorithms are limited. For example, time-of-flight (ToF) methods are limited to setups where boundary reflections do not affect the extraction of ToF, and damage index approaches require numerous transducers because they only deploy a few statistical features from the signals. To overcome these limitations, this thesis presents a novel machine learning (ML)-based localization algorithm that is integrated with a ray tracking-based physical model. Specifically, ray tracking is deployed to generate synthetic signals, then they are utilized to assist ML in extracting features from the actual measurements. With the features extracted, a scatterer can be accurately localized using some simple regression model, and the accuracy is superior to that of ToF methods and a convolution neural network. In addition, the algorithm only uses one actuator and two sensors that can even be placed on the boundaries. As a side product, the computational efficiency of the ray tracking algorithm is also enhanced.

In structural health monitoring or development of an ultrasonic touchscreen, one often needs to localize a Lamb wave scatterer. That is, to identify the position of an object that perturbs the field of Lamb waves. However, the applicability and the effectiveness of the existing localization algorithms are limited. For example, time-of-flight (ToF) methods are limited to setups where boundary reflections do not affect the extraction of ToF, and damage index approaches require numerous transducers because they only deploy a few statistical features from the signals. To overcome these limitations, this thesis presents a novel machine learning (ML)-based localization algorithm that is integrated with a ray tracking-based physical model. Specifically, ray tracking is deployed to generate synthetic signals, then they are utilized to assist ML in extracting features from the actual measurements. With the features extracted, a scatterer can be accurately localized using some simple regression model, and the accuracy is superior to that of ToF methods and a convolution neural network. In addition, the algorithm only uses one actuator and two sensors that can even be placed on the boundaries. As a side product, the computational efficiency of the ray tracking algorithm is also enhanced.