Data Science in Engineering Vol. 10

Physics-informed machine learning (PIML) is a methodology that combines principles from physics with machine learning (ML) techniques to enhance the accuracy and interpretability of predictive models. By incorporating physical laws and constraints into the learning process, physics-informed machine learning enables more robust predictions and reduces the need for large amounts of training data. PIML has a wide range of applications in science and engineering, such as modeling physical systems, solving partial differential equations, and performing inverse analysis and optimization.

In part I of this two-part series, the authors will provide attendees with an overview of the main concepts, methods, applications, and challenges of PIML. According to the way that a first-principle model is integrated with a data-driven ML model, it is possible to classify physics-informed strategies. In this overview, seven strategies will be covered: physics-constrained ML; physics-guided ML; physics-encoded ML; data-augmentation via physics principles; transfer learning from physics-based synthetic data to experimental data; delta-learning physics correction to improve physics generalization and delta-learning unknown physics to represent unmodeled physical phenomena. The benefits of these approaches including better generalization, explainability, and efficiency of the ML models will be addressed. This work will present related challenges and limitations of each approach. Finally, the authors will discuss some open research questions and future directions for PIML. By the end of this tutorial, the participants will have a comprehensive understanding of the principles and potential of PIML, as well as the ability to critically evaluate PIML models.

Research in machine learning (ML) for structural health monitoring (SHM) has increased in recent years due to ML’s potential to extract information from large quantities of data collected under varying conditions to make predictions, such as detection, identification, and characterization. Current ML implementation consists of training a model for narrow, task-specific needs, such as training a neural network to detect the presence of structural faults. However, advancements in ML and artificial intelligence (AI) have contributed foundation models—large models trained on broad data in a self-supervised fashion that can be quickly fine-tuned to accomplish specific downstream tasks different from the task it was trained on. For example, a foundation model that is trained for damage detection may be prompted to perform identification and characterization tasks given future data. Because the training and tasking of foundation models are inherently different from current ML implementation, metrics that capture performance while also considering these differences are needed for fair evaluation and comparison between approaches. This research focuses on the testing, evaluation, and benchmarking for foundation models trained on vibration data from ground sensors. We will present metrics that incorporate a broad series of tasks to quantify the performance of foundation models against other traditional ML models. Since the ground vibration data is employed to train and test foundation models for seismic events, the tasks of these models are well aligned with SHM: detecting, identifying, and characterizing acceleration signals or images. The comprehensive evaluation approach and metrics we present will be a step toward holistically quantifying advanced ML/AI success as it inevitably permeates the field of SHM.

The additively manufactured (AM) parts have been introduced in many industrial fields, and their usage is growing. This increase of use forces the need for effective tools for damage evaluation. This study focuses on elastic guided waves. Their propagation was analyzed, and wave scattering was used for damage assessment. The samples under investigation are flat plates printed with poly(lactic acid) (PLA). A few plates were prepared with five infill densities. Solid printed parts use a lot of material, so the reduction of the infill density allows to save material required for manufacturing. On the other hand, the reduction of the infill density makes the structure similar to a sandwich composite, and such complex structure influences the guided wave propagation behavior. In this study, plates were prepared as healthy and with simulated damage. The simulated damage was a void introduced in the printing process. The guided waves in the plates were excited with surface-mounted piezoelectric transducers, while the sensing was realized with scanning laser Doppler vibrometer. Damage localization algorithms based on wave reflections were developed, and their performance was analyzed as a function of the infill density. The obtained results show a potential of guided waves-based techniques for the structural health monitoring of additively manufactured structures.

In this work, optimal modeling of deep groove ball bearings is examined for application in multibody dynamics simulations. First, the equations for the normal contact force between the rolling elements and the two bearing races are established, including the effects of raceway surface roughness. Various contact force models with different hysteresis damping formulations are examined in order to select the best suited for the application. The bearing contact force model is then used in a multibody dynamics simulation of a bearing test-rig, aiming to estimate the model’s optimal parameters resulting in a good approximation of the system’s behavior and, finally, to a well-calibrated ready-to-use bearing model. The optimal model is then used to examine the system’s behavior in the presence of defects in the bearings, validating the robustness and performance of the optimized deep groove ball bearing model. The system’s response is examined by means of signal analysis as well as by using deep learning methods in order to characterize the health state of the system, thus proving the applicability of the present bearing modeling method for condition monitoring applications.

Fatigue assessment in bridges is crucial for maintaining the American road infrastructure. Typically, this involves measuring the bridge’s strain response under daily traffic loading. However, deploying and maintaining strain sensors is costly and labor-intensive compared to acceleration sensors. To address this issue, we propose a neural network architecture that can perform indirect sensing by estimating strain from measured acceleration response. Our proposed network employs convolutional neural networks (CNN) and transformers to account for uncertainties and noise associated with field data, and effectively convert accelerations to strain by capturing both the pseudo-static and dynamic features of the strain response. To demonstrate the effectiveness of our framework, we use field data collected from the Gene Hartzell Memorial Bridge in Easton, Pennsylvania, USA, as a case study. With our novel approach, we can estimate strain with high accuracy from acceleration data and reconstruct rainflow cycle counting diagrams that can subsequently be used for bridge condition and life cycle assessment.

Transfer learning (TL) methods have become increasingly crucial for the challenges in gathering accurately labeled data from various structures in structural health monitoring (SHM) tasks, such as structural damage detection (SDD). The structures must meet specific similitude criteria for the proposed TL technique’s effectiveness in current one-to-one domain approaches. To overcome this challenge, the authors have developed a novel TL method that utilizes raw vibrational features and raw-feature-to-raw-feature domain adaptation (DA) through spectral mapping. This approach offers a generalizable TL strategy that works across vastly different structures. The authors used generative adversarial network (GAN) architecture for the “learning,” as it can accommodate high-dimensional inputs in a zero-shot setting. The proposed TL approach was successfully evaluated over three structural health monitoring (SHM) benchmarks. Area under the curve (AUC) of the receiver operating characteristics (ROC) curve resulted in a threshold-bias-free estimation of SDD models retaining as much as 99% of the source model’s AUC through its application across different systems with diverse damage-representative data cases.

Physics-informed machine learning is a methodology that combines principles from physics with machine learning techniques to enhance the accuracy and interpretability of predictive models. By incorporating physical laws and constraints into the learning process, physics-informed machine learning enables more robust predictions and reduces the need for large amounts of training data. In part II of this two-part series, the authors present structural response forecasting using a physics-constrained methodology to solve the homogeneous second-order differential equations that constitute the equation of motion of a linear structural system. This forward problem is formulated to allow the incorporation of numerical methods into the training process while using segmented training to circumvent intrinsic stability limitations to the physics-informed machine learning problem. The ability of physics-informed machine learning to make generalizations for limited training data is discussed.

For rapid infrastructure assessment following natural and man-made emergencies, the utilization of minimally invasive and cost-effective drone deployable sensor packages has gained significant attention. While compact sensors with wireless data transfer capabilities have demonstrated potential for monitoring structural dynamics of critical infrastructure, such systems typically require data to be processed off-device and often off-site. These additional steps hinder the rapid assessment aspect. A challenge arises when transmission is not feasible due to degraded communication links during natural or man-made emergencies. Moreover, off-site data processing may add unnecessary delays to actions that can be taken by emergency personnel following infrastructure damage. To maximize the usefulness of sensor packages for rapid infrastructure assessment, the integration of edge computing techniques into the sensors themselves to analyze data in real time presents a promising solution. The objective of this work is to demonstrate edge computing for frequency-based structural health monitoring techniques to showcase the effectiveness of on-device data processing for the rapid assessment of infrastructure. The proposed approach continuously computes the power spectral density of windowed vibration measurements taken from a structure of interest that has the potential to experience further damage, for example, the monitoring of a bridge immediately after a flooding event. This work presents contributions in terms of a methodology, focusing on the hardware implementation of edge computing algorithms. Additionally, a study of the performance and resource utilization of a windowed power spectral density processing algorithm on-device is provided.

Electromechanical impedance (EMI) measurements have been used for several decades in noninvasive health monitoring across various domains. Typical EMI measurements are recorded via a bonded piezoelectric transducer, at a high-frequency range, typically 30 kHz and above. Because EMI measurements are single input single output, the peaks in these measurements can be related to either mechanical, electrical, or coupled electromechanical modes, especially at higher frequencies. An attempt to move towards understanding these higher frequency modes is made in this study. To undertake this, noncontact vibration testing is carried out using a laser Doppler vibrometer (LDV). The specimen under investigation is bonded with a piezoelectric transducer with a prescribed voltage applied across the transducer. A comparison between the peaks in a recorded EMI measurement and the noncontact measurement is presented. A better understanding of these modes can be utilized for a better association between high-frequency measurement and physical attributes. Furthermore, tracking variations can lead to physical insights and mode transitions that more accurately inform material changes (damage). This work discusses the first step in this building association by exploring the relation between directional information from the noncontact measurement and coupled electromechanical information from the EMI measurement. This chapter also highlights some challenges and future work needed to make this technique robust and versatile for different specimens.

This work extends classical tools in linear model order reduction and more recent results in the field of optimization on Riemannian manifolds to the probabilistic case, within the Bayesian framework. We present a method to draw samples from a given target distribution defined on various matrix manifolds. The collected samples can be used to propagate uncertainty on the reduction matrix and other quantities of interest.

The health of an ecosystem can be challenging to monitor due to the complex nature of environmental systems. Fortunately, the health of a local ecosystem can be inferred by monitoring key species which are indicative of the overall health of the ecosystem. Microphones have emerged as a powerful tool for detecting bird calls of these key indicator species. However, using an array of microphones to monitor a large area requires a power source at each location in addition to sensor telemetry to retrieve the data. Distributed acoustic sensing (DAS) is a promising approach for large scale monitoring as a single hardware system is used to detect signals over large distances. We propose a novel application of DAS to detect avian species for ecological health monitoring. A single DAS interrogator unit and optical fiber can collect tens of kilometers of high frequency acoustic data with the added benefit that DAS does not suffer from time synchronization errors and remote power issues like traditional microphone arrays. This work investigates the performance of DAS when used to detect bird calls, with particular focus on the Great Horned Owl (GHO), an indicator species for prey vulnerability in an ecosystem. By quantifying the performance of several DAS configurations and bird call detection approaches, we demonstrate the potential of DAS for use in ecological health monitoring applications.

Acoustic emission (AE) has gained much attention in recent years for its effectiveness in nondestructive testing and continuous monitoring of civil infrastructure. As a phenomenon, when structures are loaded, AE sensors mounted on the surface of the structure receive the waves released from the damage and convert them into electrical signals. By analyzing and evaluating these recorded signals, critical information such as type, location, time of origin, size, and orientation of the damage can be identified.

Since the whole process, which includes a massive amount of dataset, is time-consuming and needs to be automated, this study aimed to develop a machine learning–based damage estimation model that would estimate fracture characteristics of concrete and would be a pioneer for the application of real-time and automated monitoring of structures. In this scope, failure behavior of concrete samples of various strengths and sizes under loading was monitored with AE using K-nearest neighbor (KNN) algorithm. A relationship was established between the load levels and damage status of the specimens with AE features. Afterward, the model was trained and tested, and fracture characteristic results estimated by the KNN models were evaluated to reveal its feasibility.

Mobile radio frequency (RF) target localization is a widely studied field with a wide variety of applications including health monitoring of electronic devices and search and rescue. This recently has been done using a greedy approach, where a sensor is moved closer to the target after each measurement. However, this does not allow for other constraints, such as maintaining a fixed distance from the target or optimization of energy consumption. Studies in the field have used techniques such as machine learning to localize static targets with received RF signals, and dynamic targets with received RF signals combined with line-of-sight observations. A recent study simulated localization of static and dynamic targets through RF signal characterization without the need for line-of-sight observation while also maintaining the previously mentioned constraints. This was done by modeling the problem as a Partially Observable Markov Decision Process (POMDP) and was solved through the use of particle filtering and reinforcement learning. The purpose of this work is to build upon this prior study by training a deep neural network in a simulated environment and applying inference in the real world. This led to various changes to the model that better matched real-world scenarios. By defining the metric of success as the distance between the actual location of the device and the estimated location of the device, it was shown that the model was able to accurately locate static devices within the measured standard deviation of the signal strength. Future work includes the use of autonomous units such as drones, as well as extending the capabilities of the model to localize real-world dynamic targets.

Acoustic emission (AE) has recently gained a significant interest as a promising technique for monitoring damage progress in various structures including buildings, bridges, pipelines, and storage tanks. It relies on analyzing the acoustic activity, primarily associated with cracking phenomena, to assess structural integrity. However, one crucial parameter derived from AE signals is the time of arrival (ToA) of acoustic events, which is challenging to pick correctly. Accurate estimation of ToA is vital in localizing damage sources and enabling early detection of probable defects. Traditional approaches for ToA estimation often suffer from sensitivity to environmental and operational factors, such as imperfect coupling between AE transducers and the structures.

To address this challenge, this study investigates the application of a one-dimensional convolutional neural network (1D CNN) for precise ToA estimation in AE signals. Experimental data acquired during compression tests on concrete specimens were utilized to train and test the model over windows of 300 and 1024 sample points in AE waveforms. By capturing a batch of representative acoustic features defined on a time basis and monitoring their evolution over time, the model was able to estimate ToA accurately in the window with 300 sample points. This proposed deep learning–based approach demonstrated promising potential for enhancing the accuracy and reliability of damage localization and early defect detection in various structural applications.

Structural damage assessment has become a necessity in the modern era. Researchers are trying to come up with better and faster ways to regulate structures’ health since traditional nondestructive testing (NDT) methods such as visual inspection take longer time to carry out and it is sensitive to the user’s skill in operating the apparatuses. Various methods incorporating reverse algorithms have been explored with the help of machine learning; however, we found out that the use of pretrained convolutional neural network (CNN) in detecting damage has not been explored widely. In this study, an ensemble network of CNNs is built based on GoogLeNet architecture to test its capability in detecting structural damages in plates. There are two cases of plate structure being tested for the model: isotropic plate (metallic structure) and orthotropic plate (composite structure). The damage induced in those plates is simulated with a reduction in mechanical properties, that is, elastic modulus in isotropic case and multidirectional elastic modulus in orthotropic case. The models try to pinpoint the location parameters of the damage in the plate and to quantify the severity of the damage itself by getting input variables from the modal properties of the plates. From the individual models, the information is then gathered using an ensemble network which is expected to improve the overall accuracy. The results from the final model show good correlation between predicted parameters and the actual case with promising results for further research.