Sensor simulation and experimental data and artificial intelligence fusion techniques and methods

Abstract

Systems, methods, and computer program products are provided for structural analysis in non-destructive evaluations using artificial intelligence (AI). An example system includes a processor to receive experimental data associated with guided wave propagation along a pipeline, generate simulation data associated with guided wave propagation along a simulated pipeline, train a neural network machine learning model based on a training dataset to provide a trained neural network machine learning model using an adversarial training technique, where the neural network machine learning model is configured to provide an output that comprises a prediction of whether a location of a pipeline has a defect, and wherein the training dataset comprises the simulation data and the experimental data associated with guided wave propagation along the pipeline.

Description

Attorney Docket No. 06527-2600412SENSOR SIMULATION AND EXPERIMENTAL DATA AND ARTIFICIAL INTELLIGENCE FUSION TECHNIQUES AND METHODSCROSS REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of U.S. Provisional Patent Application No. 63 / 789,663 filed April 16, 2025, the disclosure of which is hereby incorporated by reference in its entirety.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0002] This invention was made with government support under 89243318CFE000003, DE-NE0009210, and DE-SC0025005, awarded by the Department of Energy. The government has certain rights in the invention.BACKGROUND1. Technical Field

[0003] This disclosure relates generally to applications of artificial intelligence (Al) and, in non-limiting embodiments or aspects, to systems, methods, and computer program products for structural analysis in non-destructive evaluations using Al.2. Technical Considerations

[0004] Artificial intelligence (Al) may refer to the capability of computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and / or decision-making. Al research is a field of research in engineering, mathematics, and computer science that develops and studies methods and software that enable machines to perceive their environment and use learning and intelligence to take actions that maximize their chances of achieving defined goals. Applications of Al include advanced web search engines, chatbots, virtual assistants, autonomous vehicles, and / or play and analysis in strategy games (e.g., chess and Go).

[0005] Machine learning (ML) is typically considered as a subfield of Al, and may refer to a field of computer science that uses statistical techniques to provide a computer system with the ability to learn (e.g., to progressively improve performance of) a task with data without the computer system being explicitly programmed to perform the task. In some instances, a machine learning model may be developed for6CJ2852.DOCX Page 1 of 53Attorney Docket No. 06527-2600412a set of data so that the machine learning model may perform a task (e.g., a task associated with a prediction) with regard to the set of data. In some instances, a machine learning model may be used to classify an outcome with regard to a condition or an event. In such examples, a prediction provided by the machine learning model may include a probability that the occurrence of the condition will take place, where the probability has been generated based on the machine learning model being trained on a large dataset. Within a subfield of machine learning, advances in the field of deep learning have allowed neural networks, a class of statistical algorithms, to surpass many previous ML approaches in performance.

[0006] However, Al classification methods may require large data sets for training of a ML model which, only after training, can be used in a real-world application. In case of problems involving structural analysis, such as monitoring of large infrastructure items, which may include pipelines, bridges, nuclear fuel systems, and / or the like, there is not a feasible way of training using methods that involve solely experimental data. In addition, simulation techniques may not be sufficiently accurate to enable training and / or predictions using experimental data.SUMMARY

[0007] Accordingly, provided are improved systems, methods, and computer program products for structural analysis in non-destructive evaluations using artificial intelligence (Al).

[0008] In some non-limiting embodiments, a method for structural analysis in nondestructive evaluations using artificial intelligence (Al), may include receiving experimental data associated with guided wave propagation along a pipeline; generating simulation data associated with guided wave propagation along a simulated pipeline; training a neural network machine learning model based on a training dataset to provide a trained neural network machine learning model using an adversarial training technique, where the neural network machine learning model is configured to provide an output that may include a prediction of whether a location of a pipeline has a defect, and the training dataset may include at least one of the following: the simulation data associated with guided wave propagation along the simulated pipeline; the experimental data associated with guided wave propagation along the pipeline; or any combination thereof; and computing a result of an inference task using the trained neural network machine learning model.6CJ2852.DOCX Page 2 of 53Attorney Docket No. 06527-2600412

[0009] In some non-limiting embodiments, a system for structural analysis in nondestructive evaluations using artificial intelligence (Al), may include: at least one processor configured to: receive experimental data associated with guided wave propagation along a pipeline; generate simulation data associated with guided wave propagation along a simulated pipeline; train a neural network machine learning model based on a training dataset to provide a trained neural network machine learning model using an adversarial training technique, where the neural network machine learning model is configured to provide an output that may include a prediction of whether a location of a pipeline has a defect, and the training dataset may include at least one of the following: the simulation data associated with guided wave propagation along the simulated pipeline; the experimental data associated with guided wave propagation along the pipeline; or any combination thereof; and compute a result of an inference task using the trained neural network machine learning model.

[0010] In some non-limiting embodiments, a computer program product for structural analysis in non-destructive evaluations using artificial intelligence (Al), may include at least one non-transitory computer-readable medium including program instructions that, when executed by at least one processor, cause the at least one processor to: receive experimental data associated with guided wave propagation along a pipeline; generate simulation data associated with guided wave propagation along a simulated pipeline; train a neural network machine learning model based on a training dataset to provide a trained neural network machine learning model using an adversarial training technique, where the neural network machine learning model is configured to provide an output that comprises a prediction of whether a location of a pipeline has a defect, and the training dataset may include at least one of the following: the simulation data associated with guided wave propagation along the simulated pipeline; the experimental data associated with guided wave propagation along the pipeline; or any combination thereof; and compute a result of an inference task using the trained neural network machine learning model.

[0011] Further non-limiting embodiments or aspects will be set forth in the following numbered clauses:

[0012] Clause 1: A method for structural analysis in non-destructive evaluations using artificial intelligence (Al), comprising: receiving experimental data associated with guided wave propagation along a pipeline; generating simulation data associated with guided wave propagation along a simulated pipeline; training a neural network6CJ2852.DOCX Page 3 of 53Attorney Docket No. 06527-2600412machine learning model based on a training dataset to provide a trained neural network machine learning model using an adversarial training technique, wherein the neural network machine learning model is configured to provide an output that comprises a prediction of whether a location of a pipeline has a defect, and wherein the training dataset comprises at least one of the following: the simulation data associated with guided wave propagation along the simulated pipeline; the experimental data associated with guided wave propagation along the pipeline; or any combination thereof; and computing a result of an inference task using the trained neural network machine learning model.

[0013] Clause 2: The method of clause 1 , further comprising: generating synthetic data associated with guided wave propagation along the simulated pipeline based on the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline; wherein the training dataset comprises the synthetic data associated with guided wave propagation along the simulated pipeline.

[0014] Clause 3: The method of clauses 1 or 2, wherein the neural network machine learning model is configured to provide an output that comprises a prediction of whether a location of a pipeline has a defect according to a plurality of classifications, wherein the classifications comprise: a first classification associated with a weld location; and a second classification associated with a location of corrosion.

[0015] Clause 4: The method of any of clauses 1-3, wherein generating the simulation data associated with guided wave propagation along the simulated pipeline comprises: generating the simulation data associated with guided wave propagation along the simulated pipeline using a finite element analysis simulation and a reduced-order modeling technique.

[0016] Clause 5: The method of any of clauses 1-4, wherein receiving the experimental data associated with guided wave propagation along the pipeline comprises: receiving the experimental data associated with guided wave propagation along a pipeline that was generated based on a procedure comprising measuring guided wave propagation along a pipeline using a plurality of fiber sensors.

[0017] Clause 6: The method of any of clauses 1 -5, further comprising: generating the training dataset based on the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with6CJ2852.DOCX Page 4 of 53Attorney Docket No. 06527-2600412guided wave propagation along the pipeline, wherein generating the training dataset comprises: applying a domain adaptation technique to the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline.

[0018] Clause 7: The method of any of clauses 1-6, wherein applying the domain adaptation technique to the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline comprises: providing the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline as inputs to a convolutional neural network to provide an output that comprises synthetic data associated with guided wave propagation along the simulated pipeline, wherein the synthetic data associated with guided wave propagation along the simulated pipeline comprises a plurality of continuous wavelet transform (CWT) spectrograms that represent guided wave propagation along the simulated pipeline.

[0019] Clause 8: A system for structural analysis in non-destructive evaluations using artificial intelligence (Al), comprising: at least one processor configured to: receive experimental data associated with guided wave propagation along a pipeline; generate simulation data associated with guided wave propagation along a simulated pipeline; train a neural network machine learning model based on a training dataset to provide a trained neural network machine learning model using an adversarial training technique, wherein the neural network machine learning model is configured to provide an output that comprises a prediction of whether a location of a pipeline has a defect, and wherein the training dataset comprises at least one of the following: the simulation data associated with guided wave propagation along the simulated pipeline; the experimental data associated with guided wave propagation along the pipeline; or any combination thereof; and compute a result of an inference task using the trained neural network machine learning model.

[0020] Clause 9: The system of clause 8, further comprising: generate synthetic data associated with guided wave propagation along the simulated pipeline based on the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline; wherein the training dataset comprises the synthetic data associated with guided wave propagation along the simulated pipeline.6CJ2852.DOCX Page 5 of 53Attorney Docket No. 06527-2600412

[0021] Clause 10: The system of clauses 8 or 9, wherein the neural network machine learning model is configured to provide an output that comprises a prediction of whether a location of a pipeline has a defect according to a plurality of classifications, wherein the classifications comprise: a first classification associated with a weld location; and a second classification associated with a location of corrosion.

[0022] Clause 11: The system of any of clauses 8-10, wherein, when generating the simulation data associated with guided wave propagation along the simulated pipeline, the at least one processor is configured to: generate the simulation data associated with guided wave propagation along the simulated pipeline using a finite element analysis simulation and a reduced-order modeling technique.

[0023] Clause 12: The system of any of clauses 8-11 , wherein, when receiving the experimental data associated with guided wave propagation along the pipeline, the at least one processor is configured to: receive the experimental data associated with guided wave propagation along a pipeline that was generated based on a procedure comprising measuring guided wave propagation along a pipeline using a plurality of fiber sensors.

[0024] Clause 13: The system of any of clauses 8-12, wherein the at least one processor is further configured to: generate the training dataset based on the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline, wherein, when generating the training dataset, the at least one processor is configured to: apply a domain adaptation technique to the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline.

[0025] Clause 14: The system of any of clauses 8-13, wherein, when applying the domain adaptation technique to the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline, the at least one processor is configured to: provide the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline as inputs to a convolutional neural network to provide an output that comprises synthetic data associated with guided wave propagation along the simulated pipeline, wherein the synthetic data associated with guided wave6CJ2852.DOCX Page 6 of 53Attorney Docket No. 06527-2600412propagation along the simulated pipeline comprises a plurality of continuous wavelet transform (CWT) spectrograms that represent guided wave propagation along the simulated pipeline.

[0026] Clause 15: A computer program product for structural analysis in nondestructive evaluations using artificial intelligence (Al), including at least one non-transitory computer-readable medium including program instructions that, when executed by at least one processor, cause the at least one processor to: receive experimental data associated with guided wave propagation along a pipeline; generate simulation data associated with guided wave propagation along a simulated pipeline; train a neural network machine learning model based on a training dataset to provide a trained neural network machine learning model using an adversarial training technique, wherein the neural network machine learning model is configured to provide an output that comprises a prediction of whether a location of a pipeline has a defect, and wherein the training dataset comprises at least one of the following: the simulation data associated with guided wave propagation along the simulated pipeline; the experimental data associated with guided wave propagation along the pipeline; or any combination thereof; and compute a result of an inference task using the trained neural network machine learning model.

[0027] Clause 16: The computer program product of clause 15, wherein the one or more instructions further cause the at least one processor to: generate synthetic data associated with guided wave propagation along the simulated pipeline based on the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline; and wherein the training dataset comprises the synthetic data associated with guided wave propagation along the simulated pipeline.

[0028] Clause 17: The computer program product of clauses 15 or 16, wherein the neural network machine learning model is configured to provide an output that comprises a prediction of whether a location of a pipeline has a defect according to a plurality of classifications, wherein the plurality of classifications comprise: a first classification associated with a weld location; and a second classification associated with a location of corrosion.

[0029] Clause 18: The computer program product of any of clauses 15-17, wherein, the one or more instructions that cause the at least one processor to generate the simulation data associated with guided wave propagation along the simulated pipeline,6CJ2852.DOCX Page 7 of 53Attorney Docket No. 06527-2600412cause the at least one processor to: generate the simulation data associated with guided wave propagation along the simulated pipeline using a finite element analysis simulation and a reduced-order modeling technique.

[0030] Clause 19: The computer program product of any of clauses 15-18, wherein, the one or more instructions that cause the at least one processor to receive the experimental data associated with guided wave propagation along the pipeline, cause the at least one processor to: receive the experimental data associated with guided wave propagation along a pipeline that was generated based on a procedure comprising measuring guided wave propagation along a pipeline using a plurality of fiber sensors.

[0031] Clause 20: The computer program product of any of clauses 15-19, wherein the at least one processor is further configured to: generate the training dataset based on the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline, wherein, the one or more instructions that cause the at least one processor to generate the training dataset, cause the at least one processor to: apply a domain adaptation technique to the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline.

[0032] Clause 21 : The computer program product of any of clauses 15-20, wherein, the one or more instructions that cause the at least one processor to apply the domain adaptation technique to the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline, cause the at least one processor to: provide the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline as inputs to a convolutional neural network to provide an output that comprises synthetic data associated with guided wave propagation along the simulated pipeline, wherein the synthetic data associated with guided wave propagation along the simulated pipeline comprises a plurality of continuous wavelet transform (CWT) spectrograms that represent guided wave propagation along the simulated pipeline.

[0033] These and other features and characteristics of the present disclosure, as well as the methods of operation and functions of the related elements of structures and the combination of parts and economies of manufacture, will become more6CJ2852.DOCX Page 8 of 53Attorney Docket No. 06527-2600412apparent upon consideration of the following description and the appended claims with reference to the accompanying drawings, all of which form a part of this specification, wherein like reference numerals designate corresponding parts in the various figures. It is to be expressly understood, however, that the drawings are for the purpose of illustration and description only and are not intended as a definition of the limits of the disclosed subject matter.BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Additional advantages and details are explained in greater detail below with reference to the non-limiting, exemplary embodiments that are illustrated in the accompanying schematic figures, in which:

[0035] FIG. 1 is a schematic diagram of a system for structural analysis in nondestructive evaluations using artificial intelligence (Al), according to some non-limiting embodiments or aspects;

[0036] FIG. 2 is a flow diagram for a process for structural analysis in nondestructive evaluations using Al, according to some non-limiting embodiments or aspects;

[0037] FIG. 3 is a diagram of a framework for structural analysis in non-destructive evaluations using Al, according to some non-limiting embodiments or aspects;

[0038] FIGS. 4A-4K are schematic diagrams of an exemplary implementation of process for structural analysis in non-destructive evaluations using Al using the framework shown in FIG. 3, according to some non-limiting embodiments or aspects; and

[0039] FIG. 5 is a schematic diagram of example components of one or more devices of FIG. 1 , according to some non-limiting embodiments or aspects.DESCRIPTION

[0040] For purposes of the description hereinafter, the terms “end,” “upper,” “lower,” “right,” “left,” “vertical,” “horizontal,” “top,” “bottom,” “lateral,” “longitudinal,” and derivatives thereof shall relate to the embodiments as they are oriented in the drawing figures. However, it is to be understood that the present disclosure may assume various alternative variations and step sequences, except where expressly specified to the contrary. It is also to be understood that the specific devices and processes illustrated in the attached drawings, and described in the following specification, are6CJ2852.DOCX Page 9 of 53Attorney Docket No. 06527-2600412simply exemplary and non-limiting embodiments or aspects of the disclosed subject matter. Hence, specific dimensions and other physical characteristics related to the embodiments or aspects disclosed herein are not to be considered as limiting.

[0041] Some non-limiting embodiments or aspects are described herein in connection with thresholds. As used herein, satisfying a threshold may refer to a value being greater than the threshold, more than the threshold, higher than the threshold, greater than or equal to the threshold, less than the threshold, fewer than the threshold, lower than the threshold, less than or equal to the threshold, equal to the threshold, etc.

[0042] No aspect, component, element, structure, act, step, function, instruction, and / or the like used herein should be construed as critical or essential unless explicitly described as such. Also, as used herein, the articles “a” and “an” are intended to include one or more items and may be used interchangeably with “one or more” and “at least one.” Furthermore, as used herein, the term “set” is intended to include one or more items (e.g., related items, unrelated items, a combination of related and unrelated items, and / or the like) and may be used interchangeably with “one or more” or “at least one.” Where only one item is intended, the term “one” or similar language is used. Also, as used herein, the terms “has,” “have,” “having,” or the like are intended to be open-ended terms. Further, the phrase “based on” is intended to mean “based at least partially on” unless explicitly stated otherwise. In addition, reference to an action being “based on” a condition may refer to the action being “in response to” the condition. For example, the phrases “based on” and “in response to” may, In some non-limiting embodiments, refer to a condition for automatically triggering an action (e.g., a specific operation of an electronic device, such as a computing device, a processor, and / or the like).

[0043] As used herein, the term “communication” may refer to the reception, receipt, transmission, transfer, provision, and / or the like of data (e.g., information, signals, messages, instructions, commands, and / or the like). For one unit (e.g., a device, a system, a component of a device or system, combinations thereof, and / or the like) to be in communication with another unit means that the one unit is able to directly or indirectly receive information from and / or transmit information to the other unit. This may refer to a direct or indirect connection (e.g., a direct communication connection, an indirect communication connection, and / or the like) that is wired and / or wireless in nature. Additionally, two units may be in communication with each other6CJ2852.DOCX Page 10 of 53Attorney Docket No. 06527-2600412even though the information transmitted may be modified, processed, relayed, and / or routed between the first and second units. For example, a first unit may be in communication with a second unit even though the first unit passively receives information and does not actively transmit information to the second unit. As another example, a first unit may be in communication with a second unit if at least one intermediary unit processes information received from the first unit and communicates the processed information to the second unit.

[0044] As used herein, the term “computing device” may refer to one or more electronic devices configured to process data. A computing device may, in some examples, include the necessary components to receive, process, and output data, such as a processor, a display, a memory, an input device, a network interface, and / or the like. A computing device may be a mobile device. As an example, a mobile device may include a cellular phone (e.g., a smartphone or standard cellular phone), a portable computer, awearable device (e.g., watches, glasses, lenses, clothing, and / or the like), a personal digital assistant (PDA), and / or other like devices. A computing device may also be a desktop computer or other form of non-mobile computer.

[0045] As used herein, the term “server” may refer to or include one or more computing devices that are operated by or facilitate communication and processing for multiple parties in a network environment, such as the Internet, although it will be appreciated that communication may be facilitated over one or more public or private network environments and that various other arrangements are possible. Further, multiple computing devices (e.g., servers, user devices, such as mobile devices, etc.) directly or indirectly communicating in the network environment may constitute a “system.”

[0046] As used herein, the term “system” may refer to one or more computing devices or combinations of computing devices (e.g., processors, servers, client devices, software applications, components of such, and / or the like). Reference to “a device,” “a server,” “a processor,” and / or the like, as used herein, may refer to a previously-recited device, server, or processor that is recited as performing a previous step or function, a different device, server, or processor, and / or a combination of devices, servers, and / or processors. For example, as used in the specification and the claims, a first device, a first server, or a first processor that is recited as performing a first step or a first function may refer to the same or different device, server, or processor recited as performing a second step or a second function.6CJ2852.DOCX Page 11 of 53Attorney Docket No. 06527-2600412

[0047] Pipelines form the backbone of modern energy and / or utility infrastructure by transporting oil, gas, and other critical resources across thousands of kilometers under diverse operational and environmental conditions. The integrity of pipelines is directly tied to public safety, environmental protection, and economic continuity. Corrosion, cracking, and / or wall-thinning represent pervasive threats to pipelines, often developing insidiously beneath coatings or insulation and leading to catastrophic failures when undetected. According to recent industry surveys, corrosion alone accounts for nearly half of all recorded pipeline incidents worldwide, with annual losses in the oil and gas sector exceeding billions of dollars in repair costs, product loss, and environmental remediation. The scale of this challenge has elevated corrosion monitoring and pipeline integrity assessment to a priority area within structural health monitoring (SHM) and non-destructive evaluation (NDE).

[0048] Embodiments of the present disclosure may advance the state of guided wave SHM by developing efficient reduced-order models, simulation to real-world domain adaptation techniques, and an integrated monitoring architecture that together enable scalable, intelligent, reliable monitoring of pipelines and other critical infrastructure. The ability of guided waves to interact strongly with geometric discontinuities (e.g., welds, bends, supports, and pipe ends) may further enhance utility in practice. Consequently, guided waves have become widely adopted across the oil and gas industry, with commercial tools and permanently installed systems deployed for both periodic inspection and continuous monitoring.

[0049] The transition from inspection-based to monitoring-based paradigms has been accelerated by advances in guided wave monitoring systems (e.g., permanently installed transducer arrays), as well as a drive towards automation in SHM. Permanently installed guided wave monitoring systems may provide continuous coverage, reduced reliance on manual inspection campaigns, and / or improved detection of time-varying or transient damage processes. However, reliability of permanently installed guided wave monitoring systems depends on the ability to interpret complex guided wave signals, which are inherently contaminated by noise and influenced by environmental and operational variability. For example, coherent noise arising from transducer imbalance and pipeline geometry can mask or distort corrosion signals, while random noise stemming from instrumentation or environmental fluctuations may reduce the signal-to-noise ratio. Accurately6CJ2852.DOCX Page 12 of 53Attorney Docket No. 06527-2600412distinguishing true corrosion reflections from these noise sources remains a central challenge for guided wave SHM.

[0050] Additionally, fiber optic sensing technologies may provide for distributed and large-scale SHM. Alternative fiber optic sensors based on in-fiber structures and devices, such as Fiber Bragg Gratings (FBGs) and no-core fiber (NCF) sensors, offer compact, sensitive, and multiplexable solutions. Due to the ability for spatially distributive monitoring, fiber optic sensing technologies may be particularly well-suited for integration with guided wave excitation to provide hybrid monitoring platforms. Combining fiber optic sensors with guided wave techniques may allow for the fusion of the high sensitivity of ultrasonic interrogation with the broad coverage of multiplexed fiber optic acoustic sensors. Such hybrid systems may allow optical sensing and acoustics to converge for continuous, comprehensive corrosion detection.

[0051] In some instances, NDE approaches may remain heavily reliant on periodic in-line inspections using magnetic flux leakage and / or instrumented pipeline pigs, which may include ultrasonics. While effective for detecting large corrosion, these methods may be costly, interrupt operations, and / or lack temporal resolution necessary for real-time monitoring. Permanently installed guided wave systems may address some of these limitations, but may require robust models capable of distinguishing corrosion signals from noise and environmental variability over long lifetimes. Fiber optic distributed acoustic sensing (DAS) systems offer scalability but introduce challenges in signal interpretation likely attributable to the indirect nature of the measurements, sensitivity to environmental perturbations, and / or the massive data volumes generated. As such, despite technological advances, significant barriers hinder effective deployment of guided wave and fiber optic SHM systems for pipeline corrosion detection with data management and analytics being a need.

[0052] Machine learning (ML) methods may be a component in SHM research. Deep learning models, for instance, may provide the ability to extract features and classify structural states, including corrosion, with high accuracy, showing superior performance compared to other (e.g., handcrafted) signal processing methods. It is noteworthy that some current solutions address data from traditional NDE sensing technologies (e.g., standard ultrasonics or visual inspection) and not the unique datasets and challenges associated with fiber optic sensors. However, such approaches may require large quantities of labeled experimental data for training, which is impractical in many SHM applications. Further, deep learning models trained6CJ2852.DOCX Page 13 of 53Attorney Docket No. 06527-2600412on simulation data often fail to generalize to real experimental conditions attributable to a fidelity gap (e.g., the so-called “sim-to-real” gap). This fidelity gap may arise because high-fidelity simulations may capture the underlying wave physics but may also omit important features of experimental data, such as realistic noise, environmental conditions, and / or system degradations. Bridging this fidelity gap may allow for simulation data to be used effectively for training ML models in pipeline monitoring.

[0053] Finite Element Analysis (FEA) has long been employed to simulate guided wave propagation in pipelines by providing detailed insight into wave-corrosion interactions. However, while FEA can accurately model the physics, the computational cost may be prohibitive for large-scale parametric studies and / or real-time applications. High-resolution FEA models require fine spatial and temporal discretization to capture complexities of wave propagation, often leading to runtimes of hours or days per simulation. With this, in some non-limiting embodiments, reduced-order modeling (ROM) may be used for enabling efficient models that retain physical accuracy, while dramatically reducing computational demands. Reduced-order modeling techniques, which may include tensor decomposition and / or polynomial interpolation may allow for compressing the solution space of FEA models, thereby enabling rapid generation of synthetic signals for ML models.

[0054] The convergence of physics-based modeling, fiber optic sensing, and ML models may provide for integrating distributed sensing data with constructed digital twins of pipelines (e.g., virtual replicas that continuously assimilate data from sensors), simulations, and ML models to estimate system state in real-time. In the context of pipeline corrosion detection, a digital twin can be used to provide probabilistic estimates of corrosion occurring and level of severity, as well as future degradation. Digital twins may allow for predictive maintenance, allowing operators to forecast degradation, assess reliability, and / or make data-driven decisions. Integration of guided wave and fiber optic measurements for real-time monitoring and compensation for environmental and operational variability can be an important contributor to enhance capabilities of a digital twin framework. As a first step toward that vision, the work focuses on providing reliable real-time estimates of pipeline’s current state to inform the digital twin. Compared to traditional model-assisted reliability methods, a digital twin framework offers dynamic, adaptive monitoring that evolves with the system over the lifecycle of the system.6CJ2852.DOCX Page 14 of 53Attorney Docket No. 06527-2600412

[0055] As such, the monitoring of infrastructure is a problem of immense industrial importance and societal relevance, where guided waves, fiber optic sensing, and machine learning can be utilized together to each address different facets of this problem. Guided waves may deliver sensitivity to localized corrosion but struggle with noise and environmental effects. Fiber optic sensing offers scalability but requires advanced interpretation. ML may provide data-driven intelligence but is limited by data scarcity and the fidelity gap. The integration of these technologies into a unified monitoring system, which can ultimately be integrated in robust, digital twin based operational systems, represents an opportunity to achieve reliable, real-time pipeline corrosion detection. Accordingly, embodiments of the present disclosure provide scalable and intelligent monitoring solutions for critical infrastructure, such as pipelines. In some non-limiting embodiments, the present disclosure provides efficient reduced-order models for rapid simulation and introduces robust simulation to real-world domain adaptation techniques to effectively leverage synthetic data, thereby bridging the gap between simulation and real-world application (e.g., between the simulation domain and the experimental domain). Accordingly, the present disclosure provides a novel approach to SHM using ultrasonic inline pipeline inspection with affixed transducers, which may involve the use of optical fiber sensors in various configurations for continuous monitoring.

[0056] Non-limiting embodiments or aspects of the disclosed subject matter are directed to methods, systems, and computer program products for structural analysis in non-destructive evaluations using Al. The disclosed subject matter may include a method that includes training a neural network machine learning model based on a training dataset to provide a trained neural network machine learning model using an adversarial training technique, where the neural network machine learning model is configured to provide an output that comprises a prediction of whether a location of a pipeline has a defect. In some non-limiting embodiments, the training dataset may include at least one of the following simulation data associated with guided wave propagation along a simulated pipeline, experimental data associated with guided wave propagation along the pipeline, or any combination thereof. In some non-limiting embodiments, the method may further include computing a result of an inference task using the trained neural network machine learning model. In some non-limiting embodiments, the method may further include generating or receiving the experimental data associated with guided wave propagation along the pipeline and / or6CJ2852.DOCX Page 15 of 53Attorney Docket No. 06527-2600412generating or receiving the simulation data associated with guided wave propagation along the simulated pipeline.

[0057] In some non-limiting embodiments, the method may further include generating synthetic experimental data associated with guided wave propagation along the simulated pipeline based on the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline. In some non-limiting embodiments, the training dataset may include the synthetic experimental data associated with guided wave propagation along the simulated pipeline.

[0058] In some non-limiting embodiments, the neural network machine learning model is configured to provide an output that comprises a prediction of whether a location of a pipeline has a defect according to a plurality of classifications. In some non-limiting embodiments, the classifications may include a first classification associated with a weld location and a second classification associated with a location of corrosion.

[0059] In some non-limiting embodiments, generating the simulation data associated with guided wave propagation along the simulated pipeline may include generating the simulation data associated with guided wave propagation along the simulated pipeline using a finite element analysis simulation and a reduced-order modeling technique.

[0060] In some non-limiting embodiments, receiving the experimental data associated with guided wave propagation along the pipeline may include receiving the experimental data associated with guided wave propagation along the pipeline that was generated based on a procedure comprising measuring guided wave propagation along a pipeline using a plurality of fiber sensors.

[0061] In some non-limiting embodiments, the method may further include generating the training dataset based on the simulation data associated with guided wave propagation along a pipeline and the experimental data associated with guided wave propagation along a pipeline. In some non-limiting embodiments, generating the training dataset may include applying a domain adaptation technique to the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline.

[0062] In some non-limiting embodiments, applying the domain adaptation technique to the simulation data associated with guided wave propagation along the6CJ2852.DOCX Page 16 of 53Attorney Docket No. 06527-2600412simulated pipeline and the experimental data associated with guided wave propagation along the pipeline may include providing the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline as inputs to a convolutional neural network to provide an output that comprises synthetic experimental data associated with guided wave propagation along the simulated pipeline. In some non-limiting embodiments, the synthetic experimental data associated with guided wave propagation along the simulated pipeline comprises a plurality of continuous wavelet transform (CWT) spectrograms that represent guided wave propagation along the simulated pipeline.

[0063] In this way, the present disclosure provides for enabling real-time monitoring of critical infrastructure accurately and efficiently, including pipelines in oil and gas transportation and the various threats faced by pipelines, including human error, environmental factors, material corrosion, and / or the like.

[0064] Referring now to FIG. 1 , shown is system 100 for structural analysis in nondestructive evaluations using Al, according to some non-limiting embodiments or aspects. For example, system 100 may include structural analysis system 102, database 104, user device 106, and communication network 108.

[0065] Structural analysis system 102 may include one or more devices capable of receiving information from and / or communicating information to database 104 and / or user device 106 (e.g., directly via wired or wireless communication connection, indirectly via communication network 108, and / or the like). For example, structural analysis system 102 may include a computing device, such as a server, a group of servers, a desktop computer, a portable computer, a mobile device, and / or other like devices. In some non-limiting embodiments, structural analysis system 102 may be in communication with a data storage device (e.g., database 104), which may be local or remote to structural analysis system 102. In some non-limiting embodiments, structural analysis system 102 may be capable of receiving information from, storing information in, communicating information to, or searching information stored in the data storage device (e.g., database 104).

[0066] Database 104 may include one or more devices capable of receiving information from and / or communicating information to structural analysis system 102 and / or user device 106 (e.g., directly via wired or wireless communication connection, indirectly via communication network 108, and / or the like). For example, database 1046CJ2852.DOCX Page 17 of 53Attorney Docket No. 06527-2600412may include a computing device, such as a server, a group of servers, a desktop computer, a portable computer, a mobile device, and / or other like devices. In some non-limiting embodiments, database 104 may include a data storage device. In some non-limiting embodiments, database 104 may be capable of receiving information from, storing information in, communicating information to, or searching information stored in the data storage device. In some non-limiting embodiments, database 104 may be part of structural analysis system 102 and / or part of the same system as structural analysis system 102.

[0067] User device 106 may include one or more devices capable of receiving information from and / or communicating information to structural analysis system 102 and / or database 104 (e.g., directly via wired or wireless communication connection, indirectly via communication network 108, and / or the like). For example, user device 106 may include a computing device, such as a mobile device, a portable computer, a desktop computer, and / or other like devices. Additionally or alternatively, each user device 106 may include a device capable of receiving information from and / or communicating information to other user devices 106 (e.g., directly via wired or wireless communication connection, indirectly via communication network 108, and / or the like). In some non-limiting embodiments, user device 106 may be part of structural analysis system 102 and / or part of the same system as structural analysis system 102. For example, structural analysis system 102, database 104, and user device 106 may all be (and / or be part of) a single system and / or a single computing device.

[0068] Communication network 108 may include one or more wired and / or wireless networks. For example, communication network 108 may include a cellular network (e.g., a long-term evolution (LTE®) network, a third generation (3G) network, a fourth generation (4G) network, a fifth generation (5G) network, a code division multiple access (CDMA) network, and / or the like), a public land mobile network (PLMN), a local area network (LAN), a wide area network (WAN), a metropolitan area network (MAN), a telephone network (e.g., the public switched telephone network (PSTN)), a private network (e.g., a private network associated with a transaction service provider), an ad hoc network, an intranet, the Internet, a fiber optic-based network, a cloud computing network, and / or the like, and / or a combination of these or other types of networks.

[0069] The number and arrangement of systems and devices shown in FIG. 1 are provided as an example. There may be additional systems and / or devices, fewer systems and / or devices, different systems and / or devices, and / or differently arranged6CJ2852.DOCX Page 18 of 53Attorney Docket No. 06527-2600412systems and / or devices than those shown in FIG. 1. Furthermore, two or more systems or devices shown in FIG. 1 may be implemented within a single system or device, or a single system or device shown in FIG. 1 may be implemented as multiple, distributed systems or devices. Additionally or alternatively, a set of systems (e.g., one or more systems) or a set of devices (e.g., one or more devices) of system 100 may perform one or more functions described as being performed by another set of systems or another set of devices of system 100.

[0070] Referring now to FIG. 2, shown is a flow diagram for process 200 for structural analysis in non-destructive evaluations using Al, according to some nonlimiting embodiments or aspects. The steps shown in FIG. 2 are for example purposes only. It will be appreciated that additional, fewer, different, and / or different order of steps may be used in non-limiting embodiments or aspects. In some non-limiting embodiments, a step may be automatically performed in response to performance and / or completion of a prior step. In some non-limiting embodiments, one or more of the steps of process 200 may be performed (e.g., completely, partially, and / or the like) by structural analysis system 102 (e.g., at least one computing device of structural analysis system 102). In some non-limiting embodiments, one or more of the steps of process 200 may be performed (e.g., completely, partially, and / or the like) by another system, another device, another group of systems, or another group of devices, separate from or including structural analysis system 102, such as database 104, user device 106, and / or the like.

[0071] As shown in FIG. 2, at step 202, process 200 may include receiving experimental data. For example, structural analysis system 102 may receive experimental data associated with guided wave propagation along a pipeline (e.g., a real pipeline, such as a physical pipe) from database 104 and / or user device 106. In some non-limiting embodiments, structural analysis system 102 may receive a dataset that includes a plurality of data records including the experimental data from database 104. In some non-limiting embodiments, the dataset may include a plurality of data records associated with a plurality of events associated with guided wave propagation along the pipeline. In some non-limiting embodiments, each data record may include information recorded by a plurality of sensors.

[0072] In some non-limiting embodiments, structural analysis system 102 may generate the experimental data associated with guided wave propagation along the pipeline. For example, the experimental data associated with guided wave propagation6CJ2852.DOCX Page 19 of 53Attorney Docket No. 06527-2600412along the pipeline may be generated based on a procedure comprising measuring guided wave propagation along a pipeline using a plurality of fiber sensors (e.g., as described below with regard to implementation 400 in FIGS. 4A-4K).

[0073] As shown in FIG. 2, at step 204, process 200 may include receiving simulation data. For example, structural analysis system 102 may receive simulation data associated with guided wave propagation along a simulated pipeline from database 104 and / or user device 106. In some non-limiting embodiments, structural analysis system 102 may generate the simulation data associated with guided wave propagation along the simulated pipeline. For example, structural analysis system 102 may generate the simulation data associated with guided wave propagation along the simulated pipeline using a finite element analysis simulation and a reduced-order modeling technique (e.g., as described below with regard to implementation 400 in FIGS. 4A-4K). In some non-limiting embodiments, the simulated pipeline may be based on (e.g., may be the same as or similar to) the pipeline, based upon which experimental data was generated.

[0074] As shown in FIG. 2, at step 206, process 200 may include generating synthetic data. For example, structural analysis system 102 may generate synthetic data associated with guided wave propagation along the simulated pipeline based on the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline (e.g., as described below with regard to implementation 400 in FIGS. 4A-4K).

[0075] In some non-limiting embodiments, structural analysis system 102 may apply a domain adaptation technique to the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline. In some non-limiting embodiments, when applying the domain adaptation technique to the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline, structural analysis system 102 may provide the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline as inputs to a convolutional neural network to provide an output that comprises synthetic data associated with guided wave propagation along the simulated pipeline, wherein the synthetic data associated with guided wave6CJ2852.DOCX Page 20 of 53Attorney Docket No. 06527-2600412propagation along the simulated pipeline comprises a plurality of CWT spectrograms that represent guided wave propagation along the simulated pipeline.

[0076] As shown in FIG. 2, at step 208, process 200 may include training an object detection machine learning model using an adversarial training technique. For example, structural analysis system 102 may train a neural network machine learning model based on a training dataset to provide a trained neural network machine learning model using an adversarial training technique (e.g., as described below with regard to implementation 400 in FIGS. 4A-4K). In some non-limiting embodiments, the neural network machine learning model may be configured to provide an output that comprises a prediction of whether a location of a pipeline has a defect.

[0077] In some non-limiting embodiments, the training dataset may include at least one of the following: the simulation data associated with guided wave propagation along the simulated pipeline, the experimental data associated with guided wave propagation along the pipeline, or any combination thereof.

[0078] In some non-limiting embodiments, structural analysis system 102 may generate the training dataset. For example, structural analysis system 102 may generate the training dataset based on the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline. In some non-limiting embodiments, when generating the training dataset, structural analysis system 102 may apply a domain adaptation technique (e.g., as described below with regard to implementation 400 in FIGS. 4A-4K) to the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline.

[0079] In some non-limiting embodiments, when applying the domain adaptation technique, structural analysis system 102 may provide the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline as inputs to a convolutional neural network to provide an output. In some non-limiting embodiments, the output may include synthetic data associated with guided wave propagation along the simulated pipeline. In some non-limiting embodiments, the synthetic data associated with guided wave propagation along the simulated pipeline may include a plurality of CWT spectrograms that represent guided wave propagation along the simulated pipeline.6CJ2852.DOCX Page 21 of 53Attorney Docket No. 06527-2600412

[0080] In some non-limiting embodiments, structural analysis system 102 may compute a result of an inference task using the trained neural network machine learning model. In some non-limiting embodiments, the inference task may include determining whether a pipeline (e.g., a physical pipeline, such as a real pipeline) has a defect. In some non-limiting embodiments, the inference task may include determining a location of a defect along a pipeline and / or providing a classification of a type of a defect.

[0081] Referring now to FIG. 3, shown is a diagram of framework 300 for structural analysis in non-destructive evaluations using Al. In some non-limiting embodiments, framework 300 (which, in some non-limiting embodiments, may be referred to as a ROM-VGG-DANN framework based on the use of reduced-order modeling (ROM), a VGG network, which may refer to a classic deep convolutional neural network (CNN) architecture developed by Oxford's Visual Geometry Group, and a domain adversarial neural network), which includes a sequential adaptation pipeline that decomposes a domain shift into three stages: reduced order modeling stage 302, neural style transfer (NST) stage 304, and progressive adversarial training stage 306. In some non-limiting embodiments, reduced-order modeling stage 302 may include Tucker decomposition and interpolation to align simulated data structurally with experimental conditions, while enabling efficient large-scale data synthesis. In some non-limiting embodiments, NST stage 304 may be applied to time-frequency representations, which incorporates realistic, position-specific noise and sensor characteristics into simulated data to provide synthetic data. In some non-limiting embodiments, progressive adversarial training stage 306 may involve the use of gradient reversal and maximum mean discrepancy (MMD) regularization, which may promote stable feature-level domain alignment.

[0082] NST stage 304 may serve as the first alignment stage, reducing perceptual differences between simulated and experimental signals by embedding realistic noise, attenuation, and / or sensor-specific effects. While NST stage 304 may make the synthetic data appear more experimentally consistent, progressive adversarial training stage 306 may be required to align latent feature distributions processed by a deep learning ML model (e.g., a deep network). In some non-limiting embodiments, progressive adversarial training stage 306 may address this by explicitly enforcing domain-invariant representations in a learned feature space. In this way, framework 300 may create a synergistic, progressive pipeline: NST narrows the low-level stylistic6CJ2852.DOCX Page 22 of 53Attorney Docket No. 06527-2600412gap at signal level, while adversarial adaptation minimizes the high-level representation gap at feature level.

[0083] Referring now to FIGS. 4A-4H, shown are diagrams of an exemplary implementation 400 of a process (e.g., process 200) for structural analysis in nondestructive evaluations using Al that involves framework 300, according to some nonlimiting embodiments. In some non-limiting embodiments, one or more of the steps of the process may be performed (e.g., completely, partially, etc.) by structural analysis system 102 (e.g., one or more devices of structural analysis system 102). In some non-limiting embodiments, one or more of the steps of the process may be performed (e.g., completely, partially, etc.) by another device or a group of devices separate from or including structural analysis system 102 (e.g., one or more devices of structural analysis system 102), database 104, and / or user device 106. In some non-limiting embodiments, FIGS. 4A-4F and the associated description may be with regard to the first stage, reduced-order modeling stage 302, of framework 300, FIG. 4G and the associated description may be with regard to the second stage, NST stage 304, of framework 300, and FIG. 4H and the associated description may be with regard to the third stage, progressive adversarial training stage 306, of framework 300.

[0084] Referring now to FIG. 4A, FIG. 4A is a diagram of an experimental setup that includes pipeline 402A and a plurality of fiber optic sensors 404A. In some nonlimiting embodiments, implementation 400 employs a dual approach, combining experimental measurements with finite element simulations to develop and validate a domain adaptation framework (e.g., framework 300), which may be used for pipeline defect detection. As shown in FIG. 4A, the experimental setup may include pipeline 402A, which may include a schedule 40, sixteen foot carbon steel pipe, which may have a 6.625-inch outer diameter, and may be equipped with a commercial magnetostrictive transceiver at a first end that generates torsional waves, such as 32 kHz torsional waves. In some non-limiting embodiments, each fiber optic sensor 404A may include, for wave detection, a no-core fiber (NCF) sensor. In some non-limiting embodiments, the plurality of fiber optic sensors 404A may be positioned at predetermined distances from excitation collar 406A. As shown in FIG. 4A, sensors 404A may be positioned at distances of 3 inches, 12 inches, 35 inches, 60 inches, 83 inches, 106 inches, 130.5 inches, and 180 inches from excitation collar 406A. As further shown in FIG. 4A, each fiber optic sensor 404A may include one or more single-6CJ2852.DOCX Page 23 of 53Attorney Docket No. 06527-2600412mode fiber (SMF) components and an NCF component, the NCF component is positioned in between two SMF components.

[0085] As further shown in FIG. 4A, the plurality of fiber optic sensors 402A may be positioned at 45-degree angles along a longitudinal axis of pipeline 402A. In this way, the experimental setup may leverage the sensitivity of the plurality of fiber optic sensors 402A to mechanical vibrations and immunity to electromagnetic interference.

[0086] In some non-limiting embodiments, to monitor the pipeline, sensors 404A may be attached using UV-curable glue applied only at splicing joints (e.g., to ensure effective acoustic coupling while maximizing flexibility). In some non-limiting embodiments, eight sensor positions may be established along pipeline 402A, spaced at approximately two to three foot intervals from excitation collar 406A. At each of the eight positions, two sensors 404A may be installed, oriented at opposing angles specifically to capture guided waves (e.g., guided waveforms) propagating through pipeline 402A. The dual-sensor, angled configuration shown in FIG. 4A, may serve the purpose of capturing different components of a strain field of a wave. This ability to process two distinct, but simultaneous, perspectives may improve the identification of subtle signals, especially from asymmetric defects (e.g., such as those 180 degrees apart circumferentially), which may not be as clearly detected by a single-angle measurement. Additionally, the dual-sensor, angled configuration may provide signal redundancy, ensuring overall system reliability by offering a data backup should a reading from a single sensor 404A become compromised.

[0087] Referring now to FIG. 4B, FIG. 4B is diagram of a finite element analysis (FEA) simulation setup that includes pipeline 402B and a plurality of fiber optic sensors 404B. Table 1 provides parameters of the simulation setup:Simulation Parameters Domain Properties ExcitationI ime Stepping Explicit Young's 210 GPa Pulse cycles: 5 methocT Module:I ime Step Size: 1 ,5e-3 ms Density: Z850 Pulse 32 kHz kg / m3 Frequency:Element Size: 0.35 in. AL ID layers: 12 Window HanningFunction:Table 1

[0088] For the FEA simulation setup, a model closely aligned with the experimental setup may be constructed. Pipeline 402B may be modeled with 12 hexahedral elements through the thickness (e.g., a thickness of 0.3 in.), adhering to guidelines of 20 elements per wavelength to ensure guided wave accuracy. The excitation signal6CJ2852.DOCX Page 24 of 53Attorney Docket No. 06527-2600412may be implemented as a 5-cycle, 32 kHz Hanning-windowed tone burst, consistent with excitation collar 406A in the experimental setup. As shown in FIG. 4B, defects may be modeled as radial notches with specified positions and depths (e.g., 10.5 in. position, 0.1 in. depth), while welds may be represented as circumferential bands with altered material properties (e.g., which may be based on experimental observations). As further shown in FIG. 4B, chart 408B provides an illustration of normalized amplitude versus time (e.g., in milliseconds) of a simulation signal that results from the FEA simulation setup.

[0089] Referring now to FIG. 4C, FIG. 4C is a diagram of Reduced-Order Model (ROM) workflow 402C that is used to generate synthetic data. In some non-limiting embodiments, the efficacy of deep learning models, particularly in complex domains like structural health monitoring (SHM), may be reliant on the availability of large, diverse, and representative training datasets. As discussed above, a significant challenge in guided wave-based monitoring is scarcity of experimental data encompassing the vast array of potential defect types, sizes, and / or locations. While high-fidelity numerical simulations, such as FEA simulations, may generate rich datasets, their computational cost may become prohibitive for creating the large, diverse, and representative training datasets required for robust deep learning, especially for a wide parametric space or considering real-time applications.

[0090] To address this, non-limiting embodiments involve the use of reduced-order models for large-scale, synthetic data generation. Reduced-order modeling may offer a computationally efficient alternative to full-order simulations and may be capable of rapidly predicting system responses, while maintaining a high degree of fidelity, particularly, for problems involving complex wave propagation phenomena. The approach is to approximate the high-dimensional spatio-temporal response of a system according to the function: f(t, x, ), where t represents time, x represents space, and represents the defect parameters from a sparse set of FEA simulations.

[0091] In some non-limiting embodiments, reduced-order modeling workflow 402C may include data collection step 412C, data factorization step 414C, data interpolation step 416C, and data reconstruction step 418C. In some non-limiting embodiments, data collection step 412C may include collecting discrete high-fidelity simulation data, f(t, x, ()3D. In some non-limiting embodiments, data factorization step 414C may include factorizing data into a core tensor and mode matrices via Tucker6CJ2852.DOCX Page 25 of 53Attorney Docket No. 06527-2600412decomposition. In some non-limiting embodiments, data interpolation step 416C may include interpolating the mode matrices for one or more new defect parameters. In some non-limiting embodiments, data reconstruction step 418C may include reconstructing a full low-rank wavefield for a new scenario, f (t,x, ")Tucker.

[0092] In some non-limiting embodiments, a reduced-order model may be generated based on Tucker tensor decomposition combined with Chebyshev polynomial interpolation. This approach compresses high dimensional spatio-temporal data into compact representations efficiently interpolated to predict new configurations, as shown in data interpolation step 416C and data reconstruction step 418C of FIG. 4C. In this way, the reduced-order model may reduce the computational resources that are otherwise necessary for high-fidelity FEA, while also maintaining accuracy in simulating guided wave propagation.

[0093] In some non-limiting embodiments, a simulation dataset (e.g., a plurality of data records, including simulation data associated with guided wave propagation along a pipeline) may be organized into a tensor (e.g., in data collection step 412C shown in FIG. 4C):

[0094] x e

[0095] where / , J, and K denote the temporal, spatial, and parametric dimensions, respectively. Tucker decomposition may be used to factorize this high-dimensional data into a smaller core tensor and a set of orthogonal mode matrices according to the formula (e.g., in data factorization step 414C):x « g x» ««> ««[X0096]3

[0097] where g E JKfixr2xr3 jsthe core tensor, andE ^n*rn are mode matrices with reduced rank rn« In. The core tensor encodes interactions among compressed bases across dimensions, while the mode matrices capture dominant patterns along time, space, and parameter axes. This decomposition provides substantial dimensionality reduction, often achieving compression ratios greater than 200:1, while preserving the essential wave physics.

[0098] To enable predictions for previously unseen parameter values, the parameter dependent mode matrix may be interpolated using Lagrange polynomials on Chebyshev nodes (e.g., in data interpolation step 416C shown in FIG. 4C). For a given parameter interval [a, b], the m Chebyshev nodes are defined as:6CJ2852.DOCX Page 26 of 53Attorney Docket No. 06527-2600412a 4- b a - b f2j 1p ~ - - -n, m[ ° 2 2 \ 2m0099] )

[0100] In some non-limiting embodiments, the corresponding Lagrange basis functions Lj (p) satisfy j (p) = 6ij ensuring exact interpolation at training points. The interpolated parameter mode matrix is then expressed as:

[0101]

[0102] This Chebyshev-based interpolation may be used over alternatives, such as uniform-grid polynomial or spline interpolation, because Chebyshev nodes minimize Runge’s oscillation phenomenon and yield superior numerical stability for smooth physical responses.

[0103] Finally, the guided wave for new parameter sets is reconstructed by combining the interpolated parameter mode matrix with the precomputed core tensor and other mode matrices (e.g., in data reconstruction step 418C shown in FIG. 4C):

[0104]

[0105] Referring now to FIG. 4D, FIG. 4D show two diagrams, one with pipeline geometry with corrosion parameters 402D (e.g., distance and width) and one with pipeline geometry with weld parameters 404D (e.g., distance and width) used as variables in reduced-order models.

[0106] Based on the reduced-order modeling approach discussed above, two separate reduced-order models may be constructed: one representing a pipeline with one or more corrosion locations and another representing a pipeline with one or more welds. Both reduced-order models may be parameterized using the same variables, as illustrated in FIG. 4D, with parameter space: p = {d,w} where d denotes defect distance (e.g., depth) and w denotes defect width. For training each reduced-order model, a 10 x 10 grid may be generated in the parameter space, resulting in 100 simulation cases for a reduced-order model associated with weld parameters and 100 simulation cases for a reduced-order model associated with corrosion parameters. Once trained, the two reduced-order models may be employed to generate an expanded dataset on a denser (e.g., 50 x 50) parameter grid. In some non-limiting embodiments, this may produce 2500 low-fidelity simulations for the a reduced-order6CJ2852.DOCX Page 27 of 53Attorney Docket No. 06527-2600412model associated with corrosion parameters and 2500 low-fidelity simulations for the a reduced-order model associated with weld parameters, resulting in a total of 5000 low-fidelity datasets. These expanded datasets may be used in subsequent training stages to provide broader coverage of a parameter space and to improve the generalization capability of a machine learning model.

[0107] A series of numerical simulations may be conducted to investigate guided wave propagation on a steel pipeline surface with varying corrosion configurations under controlled excitation. The predicted parameter ranges for corrosion and welding are summarized in Table 2:Pipeline Position (inches) Cir. Width (inches) Total Predicted Case Corrosion [5~91] [0.2, 5] 2500Welding [5~91] [0.2, 0.5] 2500Table 2

[0108] For both cases (e.g., corrosion and welding), the parameters may be sampled uniformly across the defined ranges to generate a balanced and comprehensive coverage of the parameter space. Specifically, the defect position along the pipeline may vary from 5 to 91 inches, while the circumferential width may be sampled within 0.2 to 5 inches for corrosion and within 0.2 to 0.5 inches for welding. Uniform sampling may ensure that the resulting simulation (e.g., 2500) in each category, corrosion and welding, represent an even distribution of possible configurations, thereby reducing bias in the training data and providing robust input for subsequent machine learning model development.

[0109] To ensure the synthetic data (e.g., a synthetic dataset) provides a reliable foundation for a machine learning model, the underlying reduced-order model may be validated against a high-fidelity FEA. In some non-limiting embodiments, the pipeline’s displacement field may be discretized into a grid of 10,230 nodes, with parametric studies covering varying corrosion locations and widths.

[0110] The validity of the reduced-order models (e.g., reduced-order model associated with corrosion parameters and the reduced-order model associated with welding parameters) may be established by reconstructing wavefields for defect parameters that were excluded from a training tensor. In some non-limiting embodiments, the validity of the reduced-order models (e.g., the reduced-order model associated with corrosion parameters) may be established by reconstructing6CJ2852.DOCX Page 28 of 53Attorney Docket No. 06527-2600412wavefields for defect parameters that were explicitly excluded from the training tensor, such as a corrosion defect located at 48 inches with a width of 3.84 inches.

[0111] Comparisons between the predicted response of a reduced-order model and a benchmark FEA simulation confirmed that the reduced-order model captures complex wave phenomena, including scattering, mode conversion, and reflections, with high fidelity. Quantitatively, the reduced-order model yielded a Normalized Root Mean Square Error (NRMSE) of 0.099 (approximately 9.9%) across the entire spatiotemporal domain. This metric confirms that the reduced-order model preserves the essential signal characteristics required for feature extraction in subsequent training of a machine learning model (e.g., a neural network). The primary justification for employing a reduced-order model is the tradeoff between fidelity and data scale. A high-fidelity FEA simulation may require approximately 3.5 hours per case, whereas reduced-order model may generate a sample in approximately 30 seconds. This allows for the generation of 55,000 diverse training samples, a scale which may be unattainable with FEA.

[0112] It is noted that the sufficiency of the data from a reduced-order model may not be defined necessarily by numerical adherence to FEA, but by downstream utility in a domain adaptation framework (e.g., described below, with regard to FIG. 4G). A high classification accuracy achieved on real-world experimental data may serve as validation. It confirms that the reduced-order model, while involving approximations, captures the fundamental physics that are used for a machine learning model to learn robust, generalized features that transfer effectively to a target domain (e.g., the physical domain).

[0113] In some non-limiting embodiments, data acquisition and feature space transformation may involve two defined data domains, including a source domain and a target domain. The source domain may include simulation data associated with guided wave propagation along a pipeline, which may include 1D simulated guided wave signals, such as time-corrected 1 D simulated guided wave signals. These 1 D simulated guided wave signals may be structurally aligned with the physics of the target domain. A source domain signal may be denoted as xs(t). The target domain may include data (e.g., real experimental signals) acquired from the physical pipeline. These signals are organized into position-based style libraries, where each library contains data (e.g., in the form of signals) captured at a specific sensor location. This organization may capture the unique, distance-dependent stylistic characteristics6CJ2852.DOCX Page 29 of 53Attorney Docket No. 06527-2600412(e.g., noise, attenuation, and / or dispersion) of guided wave propagation. A target domain signal can be denoted as xt(t).

[0114] For advanced signal characterization, a continuous wavelet transform (CWT) may be used to generate time-frequency representations of the experimental data (e.g., as described with regard to FIG. 4H). In some non-limiting embodiments, CWT may offer an advantage over conventional Fourier analysis for applications disclosed herein. While a Fourier Transform identifies the frequency components present in a signal, the Fourier Transform loses temporal information, which does not allow for determining when a reflection occurs. However, CWT may provide a simultaneous time-frequency decomposition, which is advantageous for two reasons, defect localization and defect characterization. Defect localization may be necessary for analyzing guided wave echoes that are both transient and arrive at different times. This preservation of temporal information may be the basis for time-of-flight calculations used to determine a physical location of a defect. With regard to defect characterization, the resulting 2D scalograms from CWT may reveal distinctive, timedependent spectral signatures for different structural elements. As shown in FIG. 4H, these signatures allow for differentiating features: benign weld signals may exhibit symmetrical energy distributions, whereas corrosion signals may show asymmetric, dispersed energy distributions, a pattern that may be used for classification.

[0115] In some non-limiting embodiments, to prepare source domain signals and target domain signals to be used in training a machine learning model (e.g., for imagebased deep learning techniques), 1D time domain signals (e.g., shown as x(t)) from both source and target domains may be transformed into 2D time-frequency representations. This is achieved using the CWT, where the CWT of a signal, x(t), is defined as the convolution of the signal with a scaled and translated version of a mother wavelet function,according to the formula:

[0117] where a is the scale parameter, which is inversely proportional to frequency, b is the translation parameter representing time,is the complex conjugate of the mother wavelet. In some non-limiting embodiments, a Morlet wavelet may be employed, which provides a balance between time and frequency resolution. This transformation produces a 2D scalogram (e.g., as shown in FIGS. 4E and 4F) where6CJ2852.DOCX Page 30 of 53Attorney Docket No. 06527-2600412the x-axis represents time, the y-axis represents frequency, and the pixel intensity represents the energy of the signal at a specific time-frequency coordinate. In some non-limiting embodiments, the 2D scalogram may include an image of size 125 x 3497 pixels.

[0118] Referring now to FIGS. 4E and 4F, FIG. 4E shows 3D scatter plot 402E of a CWT signal and 2D plot 404E of a CWT signal. In some non-limiting embodiments, the CWT signal shown in FIG. 4E may be used as a training input to a machine learning model. FIG. 4F shows initial excitation signal segment 402F, corrosion echo signal segment 404F, and welding echo signal segment 406F.

[0119] In some non-limiting embodiments, analysis of 2D scalograms demonstrated consistent differentiation between pipeline features: weld signals exhibited symmetrical energy distributions concentrated within a narrow frequency band centered at approximately 32 kHz (e.g., welding echo signal segment 406F). In this context, symmetrical may describe a signal having energy that is focused on time and evenly distributed around a single peak frequency. In contrast, corrosion signals displayed asymmetric, dispersed energy distributions spanning a broader frequency range of 26-36 kHz (e.g., corrosion echo signal segment 404F). This asymmetry may be characterized by a skew in energy towards lower frequencies and a longer temporal duration, indicating a more complex scattering interaction. This dispersion pattern in corrosion signals may be particularly significant as the T (0,1) mode employed may be theoretically non-dispersive; therefore, any observed dispersion likely indicates the presence of mode conversion resulting from structural irregularities. The initial excitation signal provides a reference baseline with its characteristic concentrated energy distribution. In some non-limiting embodiments, the 2D scalograms may be used directly as image inputs to train a convolutional neural network (CNN), a machine learning architecture designed for image classification.

[0120] Referring now to FIG. 4G, FIG. 4G shows an overview of style transfer framework 402G for guided wave corrosion detection. To align a statistical distribution of simulation data and experimental data in the form of simulated and experimental guided-wave signals, a Neural Style Transfer (NST) adapted for time-frequency representations may be used. As shown in FIG. 4G, NST may involve a pipeline for feature extraction and loss evaluation.

[0121] An objective of NST in this context may be to transform synthetic, clean spectrograms to emulate the stylistic properties of experimental data (e.g.,6CJ2852.DOCX Page 31 of 53Attorney Docket No. 06527-2600412experimental data based on a real-world pipeline), thereby bridging a gap between simulation data and experimental data (e.g., simulation data and real data). In some non-limiting embodiments, this may be accomplished by optimizing a generated image to simultaneously match the content of a simulated spectrogram (e.g., simulation data) and the style of a measured spectrogram (e.g., experimental data). A total loss function may include a weighted linear combination of two distinct components, content loss and style loss.

[0122] Content Loss (e.g., ^content) may include a term that ensures that a generated image (e.g., synthetic data) preserves the essential structural and kinematic information of an original simulated spectrogram. Content loss may be calculated by comparing feature representations from an intermediate layer of a pre-trained convolutional neural network, according to the following formula:

[0123] ’

[0124] where c" is the original content image (e.g., clean simulation), g" is the generated output image; I denotes the specific convolutional layer from which featuresare extracted;lJ Jis the activation of the i-th filter at position j in layer I. Accordingly, minimizing the content loss penalizes the generated image if its high-level content representation deviates from that of the original simulation.

[0125] Style Loss (e.g., Lstyie) may include a term that captures the textural and stylistic characteristics of the experimental data, such as noise, clutter, and / or sensor artifacts. Style is represented by the correlations between filter responses within multiple network layers, which may be captured by the Gram matrix. The Gram matrix, Gl(g" for a given layer, I, is computed as the inner product between vectorized feature maps:

[0126]

[0127] The style loss may include the weighted sum of the squared differences between the Gram matrices of the style image and the generated image across several layers:6CJ2852.DOCX Page 32 of 53Attorney Docket No. 06527-2600412V™> 1 V"1 / > >[ - 2, «>E‘where*< - WMFZ tc«® -cy®)0128]1

[0129] where s" is the style image (e.g., experimental data in the form of a measured spectrogram), Ni and Mi are the number of filters and the size of the feature map in layer I, respectively, and wi are weighting factors for the contribution of each layer to the style loss.

[0130] In some non-limiting embodiments, the Total Loss (e.g., Ltotai) may include a final objective function that combines the content and style losses to produce an image that balances structural fidelity with stylistic realism:

[0131]

[0132] In some non-limiting embodiments, the hyperparameters GJC and GJS may control the trade-off between content preservation and style transfer.

[0133] According to the NST framework shown in FIG. 4G, in the context of guided wave SHM, simulated spectrograms (e.g., simulated data) may serve as content carriers, preserving corrosion-related reflections, while experimental spectrograms (e.g., experimental data) may act as style references, embedding realistic noise and propagation variability. As shown in FIG. 4G, this adaptation provides a principled mechanism to narrow a gap between simulations and experimental (e.g., real-world) examples at a signal level. The specific balance among content, style, and variation terms was adjusted for corrosion-detection task with an emphasis placed on the methodological uniqueness of adapting an image-based NST framework to ultrasonic guided wave data and embedding it into a broader domain-adaptation pipeline.

[0134] In some non-limiting embodiments, the optimization of the trade-off parameters GJCand CJSmay be included in the NST framework, as the ratio between GJC and CJS dictates a balance between preserving the essential kinematic features of the simulation and imbuing the simulation spectrogram with realistic experimental textures. In some non-limiting embodiments, a parameter study may be conducted to determine the optimal configuration for generating high-fidelity synthetic data. A focus may be on the ratio of the content weight to the style weight, GJCI GJS.

[0135] In some non-limiting embodiments, a trade-off ratio of 1e-3 may be optimal. This configuration was found to achieve an effective balance, successfully transferring stylistic elements, such as background noise and multipath artifacts, onto the clean6CJ2852.DOCX Page 33 of 53Attorney Docket No. 06527-2600412simulation without compromising the integrity of the primary diagnostic features. Furthermore, an optimization may be performed for 2,500 iterations, a number determined to be sufficient for the loss to converge, ensuring stable and visually consistent results across synthetic data (e.g., a synthetic dataset).

[0136] Referring now to FIG. 4H, FIG. 4H is a diagram of a progressive adversarial training approach for an object detection machine learning model. As shown in FIG.4H, object detection machine learning model may be trained using synthetic data and experimental data (e.g., real data) according to an adversarial process that involves a combined loss function:rInVdI O ,7I1J $d) - MA'.* %') ~~

[0138] While preceding stages (e.g., FIGS. 4A-4F and the associated description may be with regard to the first stage, reduced-order modeling stage 302, of framework 300, FIG. 4G and the associated description may be with regard to the second stage, NST stage 304, of framework 300) may address structural alignment and pixel-level style transfer, subtle yet persistent feature-level discrepancies between domains may require adversarial learning to achieve complete domain invariance between a source domain and a target domain. The residual differences arise from complex wave propagation phenomena not fully captured by simulation, including mode conversion effects, boundary-induced reverberations, and / or nonlinear attenuation characteristics inherent to real pipeline structures.

[0139] A progressive adversarial training approach may align the feature distributions of the source domain data (e.g., simulation data) and the target domain data (e.g., experimental data) using a machine learning model that integrates a domain adversarial neural network (DANN) with a maximum mean discrepancy (MMD) metric. The DANN of the machine learning model (e.g., an object detection machine learning model) may include a feature extractor, Gf, a label predictor, Gy, and a domain classifier, Gd. The DANN may be trained via an adversarial process guided by three distinct loss functions, a label prediction loss function, a domain classification loss function, and an MMD loss function. In some non-limiting embodiments, the label prediction loss function (e.g., Ly) may be used to train the feature extractor and label predictor to accurately classify labeled source data. In some non-limiting embodiments, the label prediction loss function may include a standard supervised cross-entropy loss according to the following formula:6CJ2852.DOCX Page 34 of 53Attorney Docket No. 06527-2600412!©g(xy(.^s)J

[0140]

[0141] where Dsis the source domain dataset of m labeled samples (us, ys), where usrepresents a data sample, K is the number of classes, l[ is the indicator function, and Gt and Gyare parameterized by Of and 0y.

[0142] In some non-limiting embodiments, the domain classification loss function (e.g., Ld) may be used to train the domain classifier G to distinguish between features from the source domain and the target domain according to the following formula:&d) ™ ( fy(us) )] ( 3- "" )]

[0143] 1 v J J

[0144] where Dt is the unlabeled target domain dataset with samples ut. The domain classifier G may be trained to minimize this loss. In an adversarial setup, the feature extractor Gt may be simultaneously trained to maximize this loss, thereby learning to produce features that are indistinguishable to the domain classifier.

[0145] In some non-limiting embodiments, the MMD loss function (e.g., LMMD) may provide a direct, non-adversarial method for minimizing distance between the source domain and target domain feature distributions. The MMD loss function may measure the difference between the mean embeddings of the source domain and target domain feature distributions in a Reproducing Kernel Hilbert Space (RKHS). The squared empirical estimate is shown by the following formula:

[0146]

[0147] where Jfk is the RKHS induced by the kernel function, k. This forces the statistical properties of the source domain and target domain feature sets to align.

[0148] In some non-limiting embodiments, the parameters of the feature extractor, Of, are updated to optimize the total objective loss function (e.g., Li) that combines all three components, according to the following formula:

[0149] 6CJ2852.DOCX Page 35 of 53Attorney Docket No. 06527-2600412

[0150] The optimization seeks to minimize the label prediction loss function, Ly, to ensure task performance, to maximize the domain classification loss function, - LA to promote domain-invariance, and to minimize the MMD loss function, LMMD, to directly align feature distributions. In some non-limiting embodiments, the hyperparameters and a may be used to control the relative importance of the adversarial and the MMD alignment terms.

[0151] By optimizing the total objective loss function, Lf, this promotes stable convergence and yields improved domain adaptation performance compared to fixed-weight training. Furthermore, the phased approach prevents premature feature degradation (e.g., with is a potential instability challenge in aggressive adversarial training that can compromise the integrity of the learned features). Furthermore, the dual regularization, which combines the adversarial alignment from the gradient reversal layer (GRL) with the direct statistical alignment from the MMD metric, may provide a more robust transfer capability across a gap from simulation to real-world than either method could achieve alone.

[0152] With regard to a dataset that is used for training the object detection machine learning model, the dataset may employ a dual-domain structure designed to evaluate domain adaptation performance. In some non-limiting embodiments, a dataset (e.g., a training dataset) may include a source domain dataset and a target domain dataset.

[0153] In some non-limiting embodiments, the source domain dataset may be constructed to provide a large and diverse set of training data. In some non-limiting embodiments, the source domain dataset may include 2,200 FEA simulations with 55,000 reduced-order model simulations. Both simulation types may be generated by systematically varying key parameters within the same physical design space to ensure statistical diversity. In some non-limiting embodiments, for reproducibility, the parameter ranges may be as follows: Defect / Weld Position: Varied axially from 5 to 91 inches from an excitation point; Corrosion Circumferential Width: Randomized between 0.2 and 5.0 inches; and Welding Circumferential Width: Randomized between 0.2 and 0.5 inches.

[0154] In some non-limiting embodiments, a base set of 2,200 high-fidelity CWT spectrograms may be generated from 200 distinct pipeline configurations created using the parameters above, with signals of each configuration recorded at 11 sensor6CJ2852.DOCX Page 36 of 53Attorney Docket No. 06527-2600412positions, such as positions at 4.5, 12, 35, 60, 83, 106.5, 130.5, 144, 162, 174, and 180 inches from the excitation point. To expand this dataset efficiently, the reduced-order model (e.g., serving as a parameterized wave-propagation surrogate) may be used with the same randomized sampling procedure. In some non-limiting embodiments, the augmentation may provide 55,000 additional signals. It is noted that, while reduced-order model simulations may be lower in fidelity than FEA simulations, the signals from the reduced-order model simulations maintain essential dispersion and reflection features. Together, this dual-level data source (e.g., signals from FEA simulations and reduced-order model simulations) may balance physical accuracy with the large-scale coverage that is advantageous for deep learning, representing an extensive number of controlled yet diverse waveforms.

[0155] In some non-limiting embodiments, a target domain dataset may include authentic experimental data collected under realistic field conditions. In some nonlimiting embodiments, two pipeline configurations may be tested, and for each configuration, guided-wave responses may be recorded at the same 11 sensor positions listed above for the source domain dataset. This process may be repeated 10 times for each sensor position to capture measurement variability, yielding a total of 220 CWT spectrograms. These measurements inherently capture environmental variability and unexplainable noise absent in the simulation data. The resulting domain shift between the simulation data (e.g., simulation data that is clean, without noise) and the experimental data (e.g., experimental data that is noisy) may provide a central challenge for the described domain-adaptation framework.

[0156] Table 3 presents the partitioning of both datasets:Domain Total Samples Training Set (80%) Testing Set (20%) Source 57,200 45,760 11,440 Target 220 176 44Table 3

[0157] In some non-limiting embodiments, an 80 / 20 split may be applied and for the source domain dataset, this may result in 45,760 training and 11,440 testing samples. For the target domain, the 220 total samples may be randomly shuffled before being split into 176 training samples and 44 testing samples. This approach may ensure that the object detection machine learning model is tested on its ability to handle realistic noise and variability from the target domain. However, it is noted that the random shuffling of samples means the testing set for the target domain may6CJ2852.DOCX Page 37 of 53Attorney Docket No. 06527-2600412include repeated measurements from the same sensor positions and configurations present in the training set. With this, the evaluation may test for robustness to experimental noise rather than generalization to entirely unseen defect configurations and / or sensor locations.

[0158] CWT Spectrogram Standardization and Object Detection Classification Schema to ensure a meaningful comparison, while preserving the essential spectral characteristics for wave pattern recognition, both domains utilize consistent CWT spectrogram parameters. The analysis is conducted within a frequency range of 20-70 kHz, using 256 logarithmically spaced scales optimized for guided wave inspection, and a Morlet wavelet is selected for its optimal time-frequency localization properties. The temporal window captures complete wave propagation events with a 3.5 ms signal duration supplemented by 0.15 ms buffer zones. Furthermore, a per-sample amplitude normalization protocol is applied to a range of [0,1] to minimize intensity variations, while retaining relative wave characteristics. This process maintains high temporal resolution, which is critical for the precise detection of wave arrival times necessary for corrosion localization.

[0159] Referring now to FIG. 4I, FIG. 4I shows a schematic of pipeline setup 402I showing the relative locations of the guided wave collar, welds, and defects and 2D time-frequency representation 404I (e.g., a scalogram) that corresponds to pipeline setup 402I and is generated by applying a CWT to the 1 D time-domain signal. Red bounding boxes indicate the annotated labels for each target classification: excitation, defect, weld, and pipe end, used for training the object detection machine learning model.

[0160] As shown in FIG. 4I, framework 300 targets four distinct wave categories that correspond to critical events in pipeline inspection protocols:

[0161] Class 0: Initial Excitation Wave - Direct arrival from an ultrasonic transducer, providing an essential timing reference (t0) and system validation. Detection confirms proper sensor operation and establishes the temporal baseline for subsequent wave analysis.

[0162] Class 1 : Weld Reflections - Reflections from intentional structural joints and structurally sound (e.g., non-corroded) circumferential welds. These represent expected, benign features with predictable locations. Correctly identifying these benign features is critical to avoid false positive corrosion calls. It is important to note6CJ2852.DOCX Page 38 of 53Attorney Docket No. 06527-2600412that a weld can corrode, and in that scenario, the resulting signal may be considered a corrosion reflection and belong to Class 2.

[0163] Class 2: Corrosion Reflections - Reflections originating from structural anomalies including cracks, corrosion, and mechanical damage. This constitutes the primary target class, as accurate detection directly correlates with pipeline integrity assessment and safety risk evaluation.

[0164] Class 3: Pipe End Reflections - Strong reflections from pipeline termination points serving as signal validation landmarks and enabling assessment of overall wave attenuation characteristics.

[0165] Each CWT spectrogram may contain multiple simultaneous wave detections, with bounding box annotations defined by: Temporal Coordinates: Normalized horizontal position and width within a range of [0,1] for time-independent analysis; Frequency Coordinates: Full frequency range coverage with normalized vertical centering to accommodate various wave modes. The distinction between weld reflections (e.g., Class 1) and corrosion reflections (e.g., Class 2) may represent a challenging aspect of the classification task, as failure to differentiate these categories may lead to high false positive rates that undermine automated monitoring system reliability. While future work may involve classifying the health state of welds themselves (e.g., “healthy” vs. “corroded”), the scope of this study defines Class 1 as benign structural features and Class 2 as anomalous reflections, including corrosion. The framework disclosed herein (e.g., framework 300) specifically addresses the challenge through domain-adaptive feature learning that preserves subtle spectral differences between benign structural features and genuine corrosion across the simulation domain-to-experiment domain gap.

[0166] This dataset configuration, which contains a large-scale synthetic source domain and a limited, noisy real-world target domain, provides the necessary foundation for this domain adaptation study. The classification task maintains direct relevance to practical pipeline integrity management applications, where the cost of false positives and missed detections has significant safety and economic implications.

[0167] In some non-limiting embodiments, the domain adaptation framework may employ a three-stage training protocol to effectively bridge the gap between the simulation domain and the experimental domain, as summarized in Table 4:6CJ2852.DOCX Page 39 of 53Attorney Docket No. 06527-2600412Stage Focus Epochs Dataset Trained Components Key Parameters 1 Pre-training Feature Train: Gf, G Learning rate: 1e-3, (100 epochs) extraction & 200 SimulatedyAdam optimizer, classification only Inactive: Gd Batch size: 64 2. Domain Domain Learning rate: 5e-4, classifier discrimination Frozen: Gf, Gy(50 with frozen 150 Combined Binary crossepochs) Train: Gdfeatures entropy loss 3.Adversarial Domain-invariant Progressive GRL A fine-tuning (150 feature learning 150 Combined Train: Gf, Gy, Gd scheduling, MMD epochs) weight: 5.0Table 4

[0168] In some non-limiting embodiments, experiments may be conducted using the domain adaptation framework on a system equipped with GPUs (e.g., NVIDIA GPUs), utilizing NVIDIA CUDA® for accelerated computation. In some non-limiting embodiments, a complete CWT dataset may be loaded for the study. To ensure efficient data handling and prevent computational bottlenecks, a vectorized normalization procedure may be applied to the CWT data. In some non-limiting embodiments, each spectrogram may be individually normalized to a range of [0,1] by reshaping the data matrix for vectorized min-max scaling. This approach may accelerate preprocessing, making it suitable for large-scale experiments.

[0169] The trade-off parameters (e.g., the parameters “a" and “ ” shown in the total objective loss, Li) may be optimized in the final stage of framework 300. In the third stage, progressive adversarial training stage 306, the feature extractor Gt may be trained to minimize both the label prediction loss, Lf, and the MMD loss, Lmmd, while simultaneously being trained to maximize the domain classification loss, La, via a gradient reversal layer (GRL). This adversarial process is balanced by the MMD regularization coefficient, a, and the adversarial training weight, . These trade-off parameters may control the trade-off between classification accuracy (e.g., minimizing Ly) and domain invariance (e.g., minimizing LMMD, while maximizing La). The systematic selection of a and A, may allow for achieving optimal domain adaptation performance.

[0170] Referring now to FIG. 4J, FIG. 4J shows charts that display the transfer results of the objection detection machine learning model with different values of the trade-off parameter, a, the MMD regularization coefficient. Chart 402J shows values of MMD of extracted features for different values of the MMD regularization coefficient, and chart 404J shows values of classification accuracy for different values of the MMD6CJ2852.DOCX Page 40 of 53Attorney Docket No. 06527-2600412regularization coefficient. The MMD regularization coefficient may be evaluated across a range of {0.01, 0.05, 0.1, 0.5, 1, 5, 10, 50} through comprehensive grid search methodology, with performance assessed using dual metrics consisting of MMD distance between extracted features and classification accuracy (e.g., on experimental data).

[0171] As demonstrated in FIG. 4J, the relationship between the MMD regularization coefficient and model performance exhibited nonmonotonic behavior. To ensure the robustness of these findings and mitigate the effects of random initialization, the results shown represent average performance across five independent training trials for each parameter configuration. This methodology gives confidence that the pronounced minimum observed is a stable outcome based on optimization of the object detection machine learning model.

[0172] The charts 402J and 404J shown a trend at a = 5, where the MMD of the extracted features reached its minimum (e.g., chart 402J), indicating optimal statistical alignment between the source and target domains at this value. Correspondingly, the classification accuracy on experimental data reached its maximum of 92.12% at this same parameter setting (e.g., chart 404J). This result validates the theoretical expectation that better feature-space alignment (e.g., a smaller value of MMD) directly corresponds to higher classification accuracy, so long as the regularization is appropriately balanced. Additionally, charts 402J and 404J also show characteristics of insufficient regularization and over-regularization.

[0173] Insufficient Regularization: Values below a = 1 may fail to enforce sufficient domain alignment, leaving a large domain gap (e.g., between the simulation domain and the experimental domain) and resulting in lower accuracy.

[0174] Over-regularization: Values above a = 10 may lead to over-regularization, a state where the MMD loss component becomes overly dominant in the total objective function. This forces the model to prioritize domain invariance at the expense of its primary classification task, thereby compromising the discriminative capability and causing the observed drop in accuracy. Accordingly, the parameter a = 5 may be selected to achieve an optimal balance between domain invariance and task-specific discriminative power. This value may be established as a standard configuration for adversarial tuning experiments.6CJ2852.DOCX Page 41 of 53Attorney Docket No. 06527-2600412

[0175] In some non-limiting embodiments, optimization of the adversarial training parameter may allow for balancing domain confusion and classification performance. A comparative analysis may be conducted between progressive scheduling and fixed parameter strategies to determine the superior approach for stage 3 of framework 300.

[0176] Referring now to FIG. 4K, FIG. 4K shows charts that display transfer results of the object detection machine learning model with different values of the trade-off parameter, A, the adversarial training weight. Chart 402K shows values of MMD of extracted features for different values of the adversarial training weight and chart 404K shows values of classification accuracy for different values of the adversarial training weight.

[0177] FIG. 4K shows the performance characteristics of a fixed-parameter configuration, where fixed values of the adversarial training weight selected from {0.1 , 0.5, 1 , 5, 10} when a was maintained at the optimal value of cumulative improvement (e.g., a = 5). The results demonstrate that excessive values of the adversarial training weight, particularly those exceeding 1.0, caused performance degradation likely attributable to overly aggressive domain confusion that interfered with discriminative feature learning. In some non-limiting embodiments, the optimal fixed value of A = 1 achieved a classification accuracy of 94.33%, representing an ideal performance.

[0178] In some non-limiting embodiments, a progressive scheduling strategy may be applied, which achieved 98.12% classification accuracy, demonstrating a 3.79 percentage point improvement over the best fixed-parameter configuration. This strategy implemented the formula:

[0179] AP= 2A1 + exP (~10P)) "1

[0180] where APis the adaptive adversarial weight, and p represents the training progress, which is quantitatively defined as the ratio of the current epoch to the total number of epochs in the final 150-epoch fine-tuning stage (e.g., p = current epoch / 150). The advantage of the progressive scheduling strategy may stem from the ability to accommodate the evolving nature of feature representations during training. Early training phases may benefit from reduced domain confusion to establish stable feature extraction, while later phases require increased adversarial pressure to achieve final domain invariance.

[0181] In some non-limiting embodiments, the temporal adaptation of the adversarial training intensity may represent a methodological contribution to effective6CJ2852.DOCX Page 42 of 53Attorney Docket No. 06527-2600412domain adaptation implementation. In some non-limiting embodiments, training convergence may be monitored through complementary metrics including classification accuracy, MMD distance between domain features, and / or domain classifier confusion rate, with the domain classifier achieving approximately 50% accuracy during final stages to confirm successful domain-invariant feature learning.

[0182] Each configuration of the MMD regularization coefficient, a, and the adversarial training weight, A, may be evaluated through five independent training trials with averaged results to mitigate randomness effects, implementing early stopping criteria based on validation loss plateauing over 20 consecutive epochs and model checkpoints preserved every 50 epochs for recovery from potential divergence. In some non-limiting embodiments, the systematic optimization process demonstrated that parameter selection significantly impacts both domain adaptation effectiveness and classification performance, with the final configuration of a = 5 ( balance between domain invariance and task-specific discriminative power) and progressive A scheduling establishing a robust foundation for achieving demonstrated baseline methods performance in simulation-to-experiment transfer that provides a replicable framework for domain adaptation parameter optimization extensible to other structural health monitoring scenarios where simulation data abundance contrasts with experimental data scarcity.

[0183] Referring now to FIG. 5, shown is a diagram of example components of device 500, according to non-limiting embodiments or aspects. Device 500 may correspond to at least one of structural analysis system 102, database 104, and / or user device 106 in FIG. 1, as an example. In some non-limiting embodiments, such systems or devices in FIG. 1 may include at least one device 500 and / or at least one component of device 500. The number and arrangement of components shown in FIG. 5 are provided as an example. In some non-limiting embodiments, device 500 may include additional components, fewer components, different components, or differently arranged components than those shown in FIG. 5. Additionally or alternatively, a set of components (e.g., one or more components) of device 500 may perform one or more functions described as being performed by another set of components of device 500.

[0184] As shown in FIG. 5, device 500 may include bus 502, processor 504, memory 506, storage component 508, input component 510, output component 512,6CJ2852.DOCX Page 43 of 53Attorney Docket No. 06527-2600412and communication interface 514. Bus 502 may include a component that permits communication among the components of device 500. In some non-limiting embodiments, processor 504 may be implemented in hardware, firmware, or a combination of hardware and software. For example, processor 504 may include a processor (e.g., a central processing unit (CPU), a graphics processing unit (GPU), an accelerated processing unit (APU), etc.), a microprocessor, a digital signal processor (DSP), and / or any processing component (e.g., a field-programmable gate array (FPGA), an application-specific integrated circuit (ASIC), etc.) that can be programmed to perform a function. Memory 506 may include random access memory (RAM), read only memory (ROM), and / or another type of dynamic or static storage device (e.g., flash memory, magnetic memory, optical memory, etc.) that stores information and / or instructions for use by processor 504.

[0185] With continued reference to FIG. 5, storage component 508 may store information and / or software related to the operation and use of device 500. For example, storage component 508 may include a hard disk (e.g., a magnetic disk, an optical disk, a magneto-optic disk, a solid-state disk, etc.) and / or another type of computer-readable medium. Input component 510 may include a component that permits device 500 to receive information, such as via user input (e.g., a touch screen display, a keyboard, a keypad, a mouse, a button, a switch, a microphone, etc.). Additionally or alternatively, input component 510 may include a sensor for sensing information (e.g., a global positioning system (GPS) component, an accelerometer, a gyroscope, an actuator, etc.). Output component 512 may include a component that provides output information from device 500 (e.g., a display, a speaker, one or more light-emitting diodes (LEDs), etc.). Communication interface 514 may include a transceiver-like component (e.g., a transceiver, a separate receiver and transmitter, etc.) that enables device 500 to communicate with other devices, such as via a wired connection, a wireless connection, or a combination of wired and wireless connections. Communication interface 514 may permit device 500 to receive information from another device and / or provide information to another device. For example, communication interface 514 may include an Ethernet interface, an optical interface, a coaxial interface, an infrared interface, a radio frequency (RF) interface, a universal serial bus (USB) interface, a Wi-Fi® interface, a cellular network interface, and / or the like.6CJ2852.DOCX Page 44 of 53Attorney Docket No. 06527-2600412

[0186] Device 500 may perform one or more processes described herein. Device 500 may perform these processes based on processor 504 executing software instructions stored by a computer-readable medium, such as memory 506 and / or storage component 508. A computer-readable medium may include any non-transitory memory device. A memory device includes memory space located inside of a single physical storage device or memory space spread across multiple physical storage devices. Software instructions may be read into memory 506 and / or storage component 508 from another computer-readable medium or from another device via communication interface 514. When executed, software instructions stored in memory 506 and / or storage component 508 may cause processor 504 to perform one or more processes described herein. Additionally or alternatively, hardwired circuitry may be used in place of or in combination with software instructions to perform one or more processes described herein. Thus, embodiments described herein are not limited to any specific combination of hardware circuitry and software. The term “configured to,” as used herein, may refer to an arrangement of software, device(s), and / or hardware for performing and / or enabling one or more functions (e.g., actions, processes, steps of a process, and / or the like). For example, “a processor configured to” may refer to a processor that executes software instructions (e.g., program code) that cause the processor to perform one or more functions.

[0187] Although embodiments have been described in detail for the purpose of illustration, it is to be understood that such detail is solely for that purpose and that the disclosure is not limited to the disclosed embodiments or aspects, but, on the contrary, is intended to cover modifications and equivalent arrangements that are within the spirit and scope of the appended claims. For example, it is to be understood that the present disclosure contemplates that, to the extent possible, one or more features of any embodiment or aspect can be combined with one or more features of any other embodiment or aspect.6CJ2852.DOCX Page 45 of 53

Claims

Attorney Docket No. 06527-2600412WHAT IS CLAIMED IS:

1. A method for structural analysis in non-destructive evaluations using artificial intelligence (Al), comprising:receiving experimental data associated with guided wave propagation along a pipeline;generating simulation data associated with guided wave propagation along a simulated pipeline;training a neural network machine learning model based on a training dataset to provide a trained neural network machine learning model using an adversarial training technique, wherein the neural network machine learning model is configured to provide an output that comprises a prediction of whether a location of a pipeline has a defect, and wherein the training dataset comprises at least one of the following:the simulation data associated with guided wave propagation along the simulated pipeline;the experimental data associated with guided wave propagation along the pipeline; orany combination thereof; andcomputing a result of an inference task using the trained neural network machine learning model.

2. The method of claim 1 , further comprising:generating synthetic data associated with guided wave propagation along the simulated pipeline based on the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline;wherein the training dataset comprises the synthetic data associated with guided wave propagation along the simulated pipeline.

3. The method of claim 1, wherein the neural network machine learning model is configured to provide an output that comprises a prediction of whether a location of a pipeline has a defect according to a plurality of classifications, wherein the classifications comprise:6CJ2852.DOCX Page 46 of 53Attorney Docket No. 06527-2600412a first classification associated with a weld location; anda second classification associated with a location of corrosion.

4. The method of claim 1, wherein generating the simulation data associated with guided wave propagation along the simulated pipeline comprises:generating the simulation data associated with guided wave propagation along the simulated pipeline using a finite element analysis simulation and a reduced-order modeling technique.

5. The method of claim 1 , wherein receiving the experimental data associated with guided wave propagation along the pipeline comprises:receiving the experimental data associated with guided wave propagation along a pipeline that was generated based on a procedure comprising measuring guided wave propagation along a pipeline using a plurality of fiber sensors.

6. The method of claim 1 , further comprising:generating the training dataset based on the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline, wherein generating the training dataset comprises:applying a domain adaptation technique to the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline.

7. The method of claim 6, wherein applying the domain adaptation technique to the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline comprises:providing the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline as inputs to a convolutional neural network to provide an output that comprises synthetic data associated with guided wave propagation along the simulated pipeline, wherein the synthetic data associated with guided wave propagation along the simulated pipeline comprises a plurality of continuous wavelet6CJ2852.DOCX Page 47 of 53Attorney Docket No. 06527-2600412transform (CWT) spectrograms that represent guided wave propagation along the simulated pipeline.

8. A system for structural analysis in non-destructive evaluations using artificial intelligence (Al), comprising:at least one processor configured to:receive experimental data associated with guided wave propagation along a pipeline;generate simulation data associated with guided wave propagation along a simulated pipeline;train a neural network machine learning model based on a training dataset to provide a trained neural network machine learning model using an adversarial training technique, wherein the neural network machine learning model is configured to provide an output that comprises a prediction of whether a location of a pipeline has a defect, and wherein the training dataset comprises at least one of the following:the simulation data associated with guided wave propagation along the simulated pipeline;the experimental data associated with guided wave propagation along the pipeline; orany combination thereof; andcompute a result of an inference task using the trained neural network machine learning model.

9. The system of claim 8, further comprising:generate synthetic data associated with guided wave propagation along the simulated pipeline based on the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline;wherein the training dataset comprises the synthetic data associated with guided wave propagation along the simulated pipeline.

10. The system of claim 8, wherein the neural network machine learning model is configured to provide an output that comprises a prediction of6CJ2852.DOCX Page 48 of 53Attorney Docket No. 06527-2600412whether a location of a pipeline has a defect according to a plurality of classifications, wherein the classifications comprise:a first classification associated with a weld location; anda second classification associated with a location of corrosion.

11. The system of claim 8, wherein, when generating the simulation data associated with guided wave propagation along the simulated pipeline, the at least one processor is configured to:generate the simulation data associated with guided wave propagation along the simulated pipeline using a finite element analysis simulation and a reduced-order modeling technique.

12. The system of claim 8, wherein, when receiving the experimental data associated with guided wave propagation along the pipeline, the at least one processor is configured to:receive the experimental data associated with guided wave propagation along a pipeline that was generated based on a procedure comprising measuring guided wave propagation along a pipeline using a plurality of fiber sensors.

13. The system of claim 8, wherein the at least one processor is further configured to:generate the training dataset based on the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline, wherein, when generating the training dataset, the at least one processor is configured to:apply a domain adaptation technique to the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline.

14. The system of claim 13, wherein, when applying the domain adaptation technique to the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline, the at least one processor is configured to:6CJ2852.DOCX Page 49 of 53Attorney Docket No. 06527-2600412provide the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline as inputs to a convolutional neural network to provide an output that comprises synthetic data associated with guided wave propagation along the simulated pipeline, wherein the synthetic data associated with guided wave propagation along the simulated pipeline comprises a plurality of continuous wavelet transform (CWT) spectrograms that represent guided wave propagation along the simulated pipeline.

15. A computer program product for structural analysis in nondestructive evaluations using artificial intelligence (Al), including at least one non-transitory computer-readable medium including program instructions that, when executed by at least one processor, cause the at least one processor to:receive experimental data associated with guided wave propagation along a pipeline;generate simulation data associated with guided wave propagation along a simulated pipeline;train a neural network machine learning model based on a training dataset to provide a trained neural network machine learning model using an adversarial training technique, wherein the neural network machine learning model is configured to provide an output that comprises a prediction of whether a location of a pipeline has a defect, and wherein the training dataset comprises at least one of the following:the simulation data associated with guided wave propagation along the simulated pipeline;the experimental data associated with guided wave propagation along the pipeline; orany combination thereof; andcompute a result of an inference task using the trained neural network machine learning model.

16. The computer program product of claim 15, wherein the one or more instructions further cause the at least one processor to:6CJ2852.DOCX Page 50 of 53Attorney Docket No. 06527-2600412generate synthetic data associated with guided wave propagation along the simulated pipeline based on the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline; andwherein the training dataset comprises the synthetic data associated with guided wave propagation along the simulated pipeline.

17. The computer program product of claim 15, wherein the neural network machine learning model is configured to provide an output that comprises a prediction of whether a location of a pipeline has a defect according to a plurality of classifications, wherein the plurality of classifications comprise:a first classification associated with a weld location; anda second classification associated with a location of corrosion.

18. The computer program product of claim 15, wherein, the one or more instructions that cause the at least one processor to generate the simulation data associated with guided wave propagation along the simulated pipeline, cause the at least one processor to:generate the simulation data associated with guided wave propagation along the simulated pipeline using a finite element analysis simulation and a reduced-order modeling technique.

19. The computer program product of claim 15, wherein, the one or more instructions that cause the at least one processor to receive the experimental data associated with guided wave propagation along the pipeline, cause the at least one processor to:receive the experimental data associated with guided wave propagation along a pipeline that was generated based on a procedure comprising measuring guided wave propagation along a pipeline using a plurality of fiber sensors.

20. The computer program product of claim 15, wherein the at least one processor is further configured to:generate the training dataset based on the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data6CJ2852.DOCX Page 51 of 53Attorney Docket No. 06527-2600412associated with guided wave propagation along the pipeline, wherein, the one or more instructions that cause the at least one processor to generate the training dataset, cause the at least one processor to:apply a domain adaptation technique to the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline.

21. The computer program product of claim 20, wherein, the one or more instructions that cause the at least one processor to apply the domain adaptation technique to the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline, cause the at least one processor to:provide the simulation data associated with guided wave propagation along the simulated pipeline and the experimental data associated with guided wave propagation along the pipeline as inputs to a convolutional neural network to provide an output that comprises synthetic data associated with guided wave propagation along the simulated pipeline, wherein the synthetic data associated with guided wave propagation along the simulated pipeline comprises a plurality of continuous wavelet transform (CWT) spectrograms that represent guided wave propagation along the simulated pipeline.6CJ2852.DOCX Page 52 of 53

Images