Deep learning algorithm and electrical impedance tomography data acquisition system

Abstract

Electrical impedance tomography (EIT) is a non-destructive and non-radioactive imaging technique used to detect anomalies in materials. Deep learning (DL)-based EIT reconstruction addresses the non-linear, ill-conditioned nature of EIT inverse problems and allows for the conductivity of materials to be reconstructed directly through neural networks (NNs), as opposed to iteratively with conventional inverse reconstruction algorithms. To advance the DL-based reconstruction for EIT, a neural network (NN) architecture is trained with a custom loss function that serves as a surrogate model for the compressed sensing-based EIT reconstruction algorithm. The NN is trained to mimic a compressed sensing algorithm that performs the EIT conductivity reconstruction. The resultant NN is able to accurately capture the electrical properties and characteristics of the sensing domain when trained with limited data of varying quality, and this improves upon other DL models trained with the traditional MSE loss function.

Description

TITLE: DEEP LEARNING ALGORITHM AND ELECTRICAL IMPEDANCETOMOGRAPHY DATA ACQUISITION SYSTEMCROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority under 35 U.S.C. § 119(e) to provisional patent application U.S. Serial No. 63 / 570,412, filed March 27, 2024. The provisional patent application is hereby incorporated by reference in its entirety herein, including without limitation: the specification, claims, and abstract, as well as any figures, tables, appendices, or drawings thereof.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with government support with grant ECCS-2138756, awarded by the National Science Foundation. The government has certain rights in the invention.TECHNICAL FIELD

[0003] The present disclosure relates generally to (i) deep learning algorithms, (ii) electrical impedance tomography reconstructions, (iii) compressed sensing-based neural networks, and (iv) data acquisition systems with deep learning edge computing functionality. More particularly, but not exclusively, the present disclosure relates to autonomous damage detection and localization for materials via an electrical impedance tomography system with said edge intelligence.BACKGROUND

[0004] The background description provided herein gives context for the present disclosure. Work of the presently named inventors, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art.

[0005] Electrical impedance tomography (EIT) is an imaging technique that aims to characterize the spatial conductivity distribution in a medium using electrical voltage measurements performed along the boundary. EIT is a non-destructive, non-invasive, and nonradioactive imaging technique used for reconstructing the internal conductivity distribution ofa sensing domain. Performing EIT often requires large, stationary benchtop equipment that can be expensive and impractical. Other researchers have attempted to make portable EIT systems, but they all rely on external computation for image reconstruction / data analysis. For example, many research endeavors have been reported to develop low-cost EIT data acquisition (DAQ) systems that are more portable with smaller spatial footprints, such as the Tomo and the Spectra EIT. Researchers have also incorporated other features, such as wireless communication via Bluetooth and low power consumption. Most, if not all, portable EIT DAQ systems operate by collecting impedance or voltage data and sending it to an external computer for processing (i.e., conductivity reconstruction). The reliance on an external computer is another limitation that restricts broader applications of EIT, and this disclosure attempts to address that by transforming the traditional workflow for EIT -based damage monitoring.

[0006] Thus, there exists a need in the art for a low-cost, portable, and wireless EIT data acquisition (DAQ) system that is capable of independently performing image reconstructions on-board.

[0007] EIT has garnered increasing attention in recent years as an effective imaging technique for structural health monitoring (SHM) and medical imaging. By injecting small electrical currents across an area of interest, its internal conductivity distribution can be characterized. Such information is useful for identifying propagating cracks in concrete, monitoring lung ventilation, and even early diagnosis of tumors. Traditional methods for EIT conductivity reconstruction often utilize computationally intensive iterative algorithms. This is mainly due to the ill-posed nature of the EIT inverse problem. With recent advances in computational hardware, deep learning (DL) has been an increasingly attractive approach for EIT reconstruction as it shows potential to enhance reconstruction resolution and quality compared to traditional iterative algorithms, especially for solving non- linear ill-posed problems. However, one major drawback to DL is the reliance on large amounts of data to successfully generalize the problem at hand. Gathering large amounts of data is often extremely impractical, especially for EIT, given the number of variables involved (e.g., shape of sensing domain, number of electrodes, measurement scheme, etc.).

[0008] Thus, there also exists a need in the art to leverage a compressed sensing technique to train a neural network (NN) that performs the EIT inverse problem using only simulated training data.

[0009] Carbon fiber-reinforced polymer (CFRP) composites are widely used in aerospace, marine, and mechanical structural systems due to their extraordinary strength-to-weight ratio. However, they are subjected to various damage modes, such as mechanical damage, degradation under harsh operating conditions, and fatigue, among others. It is crucial to timely detect and even locate potential damage to facilitate efficient maintenance and to avoid catastrophic structural failures.

[0010] Many non-destructive evaluation (NDE) techniques have been developed and implemented to assess the integrity of CFRPs. For instance, ultrasonic testing uses propagating sound waves to identify anomalies in a domain by analyzing reflected waves. This approach can be challenged when it comes to complex material composition and geometry that affect sound wave propagation. Another common method is eddy current testing where a probe is used to induce eddy currents into the material and disturbances in the electromagnetic field are used to identify damage. Because this technique requires a probe to induce the eddy currents, the region of interest must be accessible, and inspection of large regions is often timeconsuming. In general, major challenges that the current state-of-the-art NDE techniques generally face include difficult analysis of complex three-dimensional (3D) structures, reliance on expensive and / or bulky equipment (z.e., high payload), and inconvenient disassembly of components for inspection which causes long operation downtime. These techniques are also fundamentally limited when it comes to embedded damage detection or real-time monitoring.

[0011] On the other hand, electrical impedance tomography (EIT) technique has recently emerged as a promising NDE approach for CFRPs, because it can directly leverage their intrinsic electrical properties. EIT is an imaging technique that can identify internal changes in conductivity of a medium by analyzing changes in voltage measured along the boundaries. Damage to CFRPs (e.g., dents, cracks, delamination, and barely visible impact damage) can directly affect the internal connectivity of the CFRPs, ultimately altering the boundary voltage measurements. The measured changes can be analyzed by the EIT algorithms to reconstruct, identify, and spatially locate those anomalies within the CFRPs.

[0012] While researchers have demonstrated the effectiveness of the EIT technique on CFRPs, there are several major limitations that hinder its broader and more practical applications. For instance, current work typically utilizes stationary and bulky benchtop equipment. Several attempts have been reported to develop more portable and compact EIT data acquisition (DAQ) systems, but they all need to transmit voltage measurements to an external computer forprocessing. This traditional workflow can be extremely inefficient for continuous condition monitoring, as most of the processed data may be insignificant (z.e., without notable damage). In addition, these EIT systems are not compatible with operating environment with limited power and computational resources (e.g., onboard monitoring of aerospace structures).

[0013] Therefore, there is also a need in the art for a novel EIT DAQ system that is not only wireless and portable, but it also includes an edge intelligence functionality enabling the device to operate as a standalone device.SUMMARY

[0014] Electrical impedance tomography (EIT) is a non-destructive and non-radioactive imaging technique used to detect anomalies in a material of interest. Applications of EIT range from medical imaging and early tumor detection to identifying structural damage. Within the past decade, deep learning (DL)-based EIT reconstruction has been an emerging field of study as it shows promise in addressing many of the challenges associated with the non-linear, ill- conditioned nature of EIT inverse problems. The DL-based approach allows for the conductivity of materials to be reconstructed directly through neural networks (NNs) as opposed to iteratively with conventional inverse reconstruction algorithms. So far, the reported DL-based NNs for EIT have mostly been trained by minimizing the mean squared error (MSE) between the predicted and “true” outputs (z.e., conductivity distributions). The performance of these current NNs heavily relies on both the quality and quantity of training data. The NNs trained with simulated data may perform poorly with experimental data. On the other hand, generating sufficient experimental data NN training can be extremely expensive and timeconsuming, if feasible at all.

[0015] For example, Figure 1A outlines a conventional workflow of applying the EIT technique for detecting structural damage by monitoring the spatial conductivity of structural materials. To be specific, the workflow generally consists of instrumenting the DAQ system, performing an EIT measurement scheme, transmitting measurements to an external device for data analysis, and inspecting for anomalies which is performed by the operator. In this workflow, data must be continuously transmitted to an external device for data processing and conductivity reconstruction. From the SHM standpoint, structural damage, especially crucial damage, may develop in an unpredictable manner, making large amounts of the data transmitted redundant (i.e., not containing any significant anomalies). For a deployable, battery-powered, and wireless DAQ system, transmitting redundant data can be highly energy-consuming, which can fundamentally limit the long- term operation of the device. Alternatively, if the DAQ system itself can identify anomalies in the material of interest, measurement data can then be selectively transmitted for further analysis. This could be a promising approach to save energy and prolong battery life.

[0016] To transform the traditional workflow for EIT-based damage monitoring, this disclosure aims to shift the resource-intensive tasks outside of the continuous monitoring stage, as shown in Figure IB. In this disclosure, a novel, portable, and low-cost EIT DAQ system with edge intelligence has been developed, enabling the system itself to perform on-board reconstructions. It is envisioned that this disclosure can significantly advance applications of EIT in the SHM of civil and aerospace structures as well as wearable technologies (e.g., for sensing prosthetics and human-machine interfaces).

[0017] To advance the DL-based reconstruction for EIT, the present disclosure further develops a novel NN architecture, trained with a custom loss function, that serves as a surrogate model for the compressed sensing-based EIT reconstruction algorithm. In other words, the NN is trained to mimic a compressed sensing algorithm that performs the EIT conductivity reconstruction. This approach enables the NN to accurately capture the electrical properties and characteristics of the sensing domain when trained with limited data of varying quality. The performance of the present NN was compared to other DL models trained with the traditional MSE loss function by evaluating their reconstruction resolution, accuracy, and other training metrics.

[0018] To show proof of concept, carbon fiber-reinforced polymer (CFRP) composites, as structural materials commonly used in aerospace, marine, and mechanical systems, are subjected to various damage modes. To timely detect the damage and avoid catastrophic structural failures, many non-destructive evaluation techniques based on different sensing modalities have been developed and implemented. One of the emerging promising techniques is electrical impedance tomography (EIT), as it can directly leverage the intrinsic electrical properties of CFRPs to detect and locate anomalies in a non-intrusive, non-radioactive, and scalable manner. However, current EIT applications are significantly hindered by their reliance on bulky benchtop data acquisition (DAQ) equipment and unlimited power and computational resources. The present disclosure aims to fundamentally advance the EIT technique by developing a novel DAQ hardware system that is not only wireless and portable, but it also includes an edge intelligence functionality enabling the system to autonomously perform dataanalysis and inform human users of the occurrence and location of potential damage. The present disclosure tackles the common challenges associated with low memory and computational capacities of edge devices by strategically designing a lightweight and robust deep learning algorithm. Through a series of comprehensive computational and experimental studies, the designed system demonstrated a high performance in detecting and locating damage on the CFRPs, regardless of different CFRP electrical properties and complex geometries. The present disclosure represents a promising step towards automating the monitoring and inspection of the integrity of CFRP structural components, which is especially valuable in the operating environment where computational resources are limited.

[0019] The present disclosure also discloses a novel EIT DAQ system that is not only wireless and portable, but it also includes an edge intelligence functionality enabling the device to operate as a standalone device. Edge intelligence refers to the decentralization of computation such that devices closer to the edge (z.e., where data is generated) can perform the analysis. The benefits of edge intelligence include lower latency computation, decongesting traffic to centralized computational hubs, and improved reliability. The present disclosure tackles the common challenges associated with low memory and computational capacities of edge devices by designing a lightweight and robust deep learning algorithm that can be deployed onto the designed DAQ hardware. This system can potentially transform the NDE workflow to help achieve autonomous condition assessment for various structural materials. The present disclosure outlines the technical backgrounds of the EIT technique and deep learning and also describes the designs of the hardware and algorithm for the proposed system. A series of computational and experimental studies is discussed to comprehensively demonstrate the performance of the hardware and deep learning algorithm developed in the present disclosure.

[0020] The following objects, features, advantages, aspects, and / or embodiments, are not exhaustive and do not limit the overall disclosure. No single embodiment need provide each and every object, feature, or advantage. Any of the objects, features, advantages, aspects, and / or embodiments disclosed herein can be integrated with one another, either in full or in part.

[0021] It is a primary object, feature, and / or advantage of the present disclosure to improve on or overcome the deficiencies in the art.

[0022] It is a further object, feature, and / or advantage of the present disclosure to demonstrate a set of benchmark tests and experiments conducted to evaluate hardware performance.

[0023] It is still yet a further object, feature, and / or advantage of the present disclosure to use findings from initial tests to help inform and guide subsequent research endeavors, which encompassed hardware redesign and the development of a deep learning-based EIT reconstruction algorithm. The redesigned system is further evaluated.

[0024] The EIT reconstruction algorithms disclosed herein can be used in a wide variety of applications. For example, with the proposed system, EIT can be performed on carbon fiber reinforced polymers to spatially locate damages. Because EIT reconstruction algorithms can be extremely computationally intensive, one such deep-learning algorithm disclosed herein leverages the compressed-sensing technique to strategically train a neural network. The proposed neural network not only achieves comparable results to traditional iterative algorithms, but does so in a fraction of the time.

[0025] It is preferred the apparatus be safe, cost effective, and durable. For example, a wireless, portable, battery-powered, and low-cost EIT DAQ system is disclosed herein.

[0026] Methods can be practiced which facilitate use, manufacture, assembly, maintenance, and repair of computational systems employing the deep learning-based EIT reconstruction algorithms which accomplish some or all of the previously stated objectives.

[0027] These and / or other objects, features, advantages, aspects, and / or embodiments will become apparent to those skilled in the art after reviewing the following brief and detailed descriptions of the drawings. The present disclosure encompasses (a) combinations of disclosed aspects and / or embodiments and / or (b) reasonable modifications not shown or described.BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Several embodiments in which the present disclosure can be practiced are illustrated and described in detail, wherein similar reference characters represent like components throughout the several views. The drawings are presented for exemplary purposes and may not be to scale unless otherwise indicated.

[0029] Figure 1A shows a workflow diagram of the conventional method applying EIT for SHM.

[0030] Figure IB shows a workflow diagram proposed in this disclosure by implementing a novel EIT DAQ system with edge intelligence for SHM.

[0031] Figure 2 shows a schematic diagram of major components in the DAQ hardware.

[0032] Figure 3 shows a physical layout of an assembled DAQ system with each major component labeled.

[0033] Figure 4 shows a schematic diagram of the adjacent current driving mode measurement scheme.

[0034] Figure 5 shows boundary voltage distribution between ABAQUS simulation and EIDORS model.

[0035] Figure 6A shows measurements 43 and 57 in the measurement frame plotted over varying anomaly conductivities.

[0036] Figure 6B shows measurements 21 and 33 in the measurement frame plotted over varying anomaly conductivities.

[0037] Figure 7A shows a schematic diagram of the resistor network for benchmark testing.

[0038] Figure 7B shows an optical image of the fabricated resistor network corresponding to Figure 7A.

[0039] Figure 8 shows a schematic diagram of a representative edge on a 16-electrode sample for illustrating the spacings of boundary electrodes.

[0040] Figure 9A shows a resistor network schematic showing current flowing into A01 and out of A32.

[0041] Figure 9B shows a resistor network schematic showing current flowing into A20 and out of A32.

[0042] Figure 9Cshows an experimental voltage distribution measured across all electrodes compared to theoretical values corresponding to Figure 9A.

[0043] Figure 9D shows an experimental voltage distribution measured across all electrodes compared to theoretical values corresponding to Figure 9B.

[0044] Figure 10 shows a comparison between unfiltered and Kalman-filtered ADC measurements within a one-second time window.

[0045] Figure 11 shows a parametric analysis of process variance regarding transient responses for Kalman filters.

[0046] Figure 12 shows a representative experimentally measured boundary voltage distribution of a 16-electrode UHMWPE sample overlapped with the theoretical values simulated from the EIT forward problem on a uniform homogenous material.

[0047] Figure 13A, Figure 13B, Figure 13C, and Figure 13D show optical images of a 16- electrode UHMWPE sample with introduced corner damages.

[0048] Figure 13E, Figure 13F, Figure 13G, and Figure 13H show conductivity distributions reconstructed using the Gauss-Newton algorithm.

[0049] Figure 131, Figure 13J, Figure 13K, and Figure 13L each show a compressed sensingTwIST algorithm corresponding to the damage scenarios in Figures 13A, Figure 13B, Figure 13C, and Figure 13D, respectively.

[0050] Figure 14 show a comparison between the Gauss-Newton and TwIST compressed sensing algorithms evaluated via blur radius.

[0051] Figure 15A, Figure 15B, Figure 15C, and Figure 15D show optical images of a 16- electrode UHMWPE sample with multiple damages on the edges.

[0052] Figure 15E, Figure 15F, Figure 15G, and Figure 15H show reconstructed conductivity distributions corresponding to the damage scenarios in Figure 15A, Figure 15B, Figure 15C, and Figure 15D, respectively.

[0053] Figure 16A, Figure 16B, and Figure 16C show optical images of a 16-electrode UHMWPE sample with multiple damages near the central regions.

[0054] Figures 16D, Figure 16E, and Figure 16F show reconstructed conductivity distributions corresponding to the damage scenarios in Figure 16A, Figure 16B, and Figure 16C, respectively.

[0055] Figures 17A, Figure 17B, Figure 17C, and Figure 17D show optical images of an 8- electrode UHMWPE sample with multiple damages on the comers.

[0056] Figures 17E, Figure 17F, Figure 17G, and Figure 17H show conductivity distributions reconstructed with the nRF52840 microcontroller.

[0057] Figures 171, Figure 17J, Figure 17K, and Figure 17L show a PC corresponding to the damage scenarios in Figures 17A, Figure 17B, Figure 17C, and Figure 17D, respectively.

[0058] Figure 18 shows a visual representation of the 1ST algorithm.

[0059] Figure 19 illustrates a visual representation of the time-unfolded 1ST inspired neural network.

[0060] Figure 20 illustrates a visual representation of the LSTMConvNet model.

[0061] Figure 21A shows a circular anomaly with its respective conductivity.

[0062] Figure 21B shows a square anomaly with its respective conductivity.

[0063] Figure 21C shows a rectangular anomaly with its respective conductivity.

[0064] Figure 21D shows a combination of all anomaly types, each with their respective conductivities.

[0065] Figure 22 shows an average pixel error plotted over epochs with varying lambda hyperparameters.

[0066] Figure 23 shows an average ACentroid plotted over epochs with varying lambda hyperparameters.

[0067] Figure 24A shows training and validation loss plotted over epochs for the compressed sensing-based neural network.

[0068] Figure 24B compares percentage differences between training and validation losses corresponding to Figure 24A.

[0069] Figure 25A shows training and validation loss plotted over epochs for the LSTMConvNet.

[0070] Figure 25B compares percentage differences between training and validation losses corresponding to Figure 25A.

[0071] Figure 26 shows a comparison between reconstruction algorithms for a representative set of data.

[0072] Figure 27 shows reconstruction results from all algorithms using experimentally collected data.

[0073] Figure 28 shows a carbon fiber test sample with surface and edge electrodes.

[0074] Figure 29 shows a CFRP plate in the 8-electrode configuration.

[0075] Figure 30A, Figure 30B, Figure 30C, and Figure 30D show optical images of the drilled through hole damage cases.

[0076] Figure 30E, Figure 30F, Figure 30G, and Figure 30H show EIT reconstructions performed with TwIST corresponding to Figure 30A, Figure 30B, Figure 30C, and Figure 30D

[0077] Figure 31A shows a reconstruction of slotted hole in CFRP with 8-electrodes.

[0078] Figure 31B shows results from an ABIQUS simulation using the reconstruction of Figure 31A.

[0079] Figure 32 shows reconstructions of partially drilled holes using the slotted hole as the baseline reference with 8-electrodes, and corresponding results from an ABIQUS simulations using said reconstructions.

[0080] Figure 33A, Figure 33B, Figure 33C, Figure 33D, Figure 33E, Figure 33F, Figure 33G, and Figure 33H show reconstructions for hammer induced impact damages on CFRP with 8- electrodes.

[0081] Figure 34 shows ABAQUS simulations for slotted holes with 8- and 16-electrodes.

[0082] Figure 35 shows a schematic diagram of the voltage-to-current converter.

[0083] Figure 36 shows a schematic of the precision rectifier measurement circuit.

[0084] Figure 37 graphs measured performance of the constant current source (CCS) under different resistance loads.

[0085] Figure 38 shows root mean squared (RMS) voltages plotted as a function of resistance load.

[0086] Figure 39 shows measured voltages versus actual voltages.

[0087] Figure 40 shows a comparison between experimentally measured 8-electrode boundary voltage and theoretical simulations with EIDORS.

[0088] Figure 41A, Figure 41B, Figure 41C, and Figure 41D show optical images of the damaged CFRP samples.

[0089] Figure 41E, Figure 41F, Figure 41G, Figure 41H show EIT reconstructions performed with TwIST corresponding to Figure 41A, Figure 41B, Figure 41C, and Figure 41D

[0090] Figure 42 shows relative changes in boundary voltage compared to undamaged baseline between partially and fully drilled holes.

[0091] Figure 43 shows reconstructions of partially and fully drilled holes in CFRP.

[0092] Figure 44 compares experimentally measured 16-electrode boundary voltage and theoretical simulations with EIDORS. Figure 44 also compares experimentally measured and simulated boundary voltage distributions on an undamaged CFRP sample.

[0093] Figure 45A, Figure 45B, Figure 45C, and Figure 45D show optical images of the damaged 16-electrode CFRP samples.

[0094] Figure 45E, Figure 45F, Figure 45G, and Figure 45H show EIT reconstructions performed with TwIST corresponding to Figure 45A, Figure 45B, Figure 45C, and Figure 45D

[0095] Figure 46A, Figure 46B, and Figure 46C show optical images of hammer induced damage onto CFRP.

[0096] Figure 46D, Figure 46E, and Figure 46F show EIT reconstructions performed with TwIST corresponding to Figure 46A, Figure 46B, and Figure 46C.

[0097] Figures 47 shows magnified images of damaged CFRP on the side opposite to where impact took place.

[0098] Figure 48A, Figure 48B, Figure 48C, and Figure 48D show optical images of chisel and hammer induced damage onto CFRP.

[0099] Figure 48E, Figure 48F, Figure 48G, and Figure 48H EIT reconstructions performed with TwIST corresponding to Figure 48A, Figure 48B, Figure 48C, and Figure 48D.

[0100] Figure 49A, Figure 49B, Figure 49C, and Figure 49D show optical images of partially drilled holes in CFRP.

[0101] Figure 49E, Figure 49F, Figure 49G, and Figure 49H show EIT reconstructions performed with CS-based NN corresponding to Figure 49A, Figure 49B, Figure 49C, and Figure 49D.

[0102] Figure 50A, Figure 50B, and Figure 50C show optical images of hammer induced damage onto CFRP.

[0103] Figures 50D, Figure 50E, and Figure 50F show EIT reconstructions performed with CS-based NN corresponding to Figure 50A, Figure 50B, and Figure 50C.

[0104] Figure 51A, Figure 51B, Figure 51C, and Figure 51D show optical images of chisel and hammer induced damage onto CFRP.

[0105] Figure 51E, Figure 51F, Figure 51G, and Figure 51H show EIT reconstructions performed with CS-based NN corresponding to Figure 51A, Figure 51B, Figure 51C, and Figure 51D.

[0106] Figure 52A shows a model of a custom printed circuit board.

[0107] Figure 52B shows an assembled DAQ system utilizing the model of the custom printed circuit board of Figure 52A.

[0108] Figure 53 shows a compressed sensing-based neural network architecture.

[0109] Figure 54 illustrates schematics of the operation of the designed DAQ system coupled with a deployed neural network (NN).

[0110] Figure 55A shows an image of the front side of the assembled DAQ hardware.

[0111] Figure 55B shows an image of the back side of the assembled DAQ hardware.

[0112] Figure 56 illustrates schematics of the architecture of the lightweight DL NN model.

[0113] Figure 57 illustrates schematics of the configuration of an example test case, where an anomaly is randomly introduced to the test domain.

[0114] Figure 58A shows an electrode setup for a planar sample.

[0115] Figure 58B shows an electrode setup for a 3D curved sample.

[0116] Figure 58C shows another view of the electrode setup for the 3D curved sample of Figure 58B.

[0117] Figure 59A shows a classification accuracy of the DL model during training over 100 epochs.

[0118] Figure 59B shows a position error of the DL model during training over 100 epochs.

[0119] Figure 59C shows a total loss of the DL model during training over 100 epochs.

[0120] Figure 60 shows a negative classification confidence of the DL model when different levels of noise were included in the voltage measurements.

[0121] Figure 61A shows an average classification confidence distribution for different combinations of anomaly size and location when anomaly conductivity changes were between 0-0.1.

[0122] Figure 61B shows an average classification confidence distribution for different combinations of anomaly size and location when anomaly conductivity changes were between 0.4-0.5.

[0123] Figure 61C shows an average classification confidence distribution for different combinations of anomaly size and location when anomaly conductivity changes were between 0.8-0.9.

[0124] Figure 62A shows an average position error distributions for a combination of anomaly size and location when anomaly conductivity changes were between 0-0.1.

[0125] Figure 62B shows an average position error distributions for a combination of anomaly size and location when anomaly conductivity changes were between 0.4-0.5.

[0126] Figure 62C shows an average position error distributions for a combination of anomaly size and location when anomaly conductivity changes were between 0.8-0.9.

[0127] Figure 63A, Figure 63B, Figure 63C, Figure 63D, and Figure 63E show damage introduced to a planar CFRP sample throughout the sequence of Figure 63A to Figure 63E, with the area and minimum distance to edge labeled for each damage case.

[0128] Figure 64A, Figure 64B, Figure 64C, Figure 64D, and Figure 64E show reconstructed conductivity distributions corresponding to damage cases shown in Figure 63 A, Figure 63B, Figure 63C, Figure 63D, and Figure 63E, respectively.

[0129] Figure 65A, Figure 65B, and Figure 65C show sequentially introduced damage on a 3D curved CFRP sample.

[0130] Figure 65D, Figure 65E, and Figure 65F show reconstructed conductivity distributions corresponding to damage cases shown in Figure 65A, Figure 65B, and Figure 65C, respectively.

[0131] Figure 66A compares classification confidences of the DL model based on experimental and simulated data of the planar CFRP sample.

[0132] Figure 66B compares position errors of the DL model based on experimental and simulated data of the planar CFRP sample.

[0133] Figure 67A compares classification confidences of the DL model based on experimental and simulated data of the curved CFRP sample.

[0134] Figure 67B compares position errors of the DL model based on experimental and simulated data of the curved CFRP sample.

[0135] An artisan of ordinary skill in the art need not view, within isolated figure(s), the near infinite distinct combinations of features described in the following detailed description to facilitate an understanding of the present disclosure.DETAILED DESCRIPTION

[0136] The present disclosure is not to be limited to that described herein. Mechanical, electrical, chemical, procedural, and / or other changes can be made without departing from the spirit and scope of the present disclosure. No features shown or described are essential to permit basic operation of the present disclosure unless otherwise indicated.Development of Electrical Impedance Tomography Data Acquisition System and Deep Learning-Based Reconstruction Algorithms for Spatial Damage DetectionForward and Inverse Problem

[0137] EIT algorithms typically include two parts, namely forward problem and inverse problem. The EIT forward problem attempts to solve for the boundary voltages of a medium (v) based on an assumed conductivity (<J) distribution. Assuming no current sources or sinks are present in the medium of interest (12), the forward problem can be formulated as7 ■ (oVv) = 0 in fl which is also known as the simplified 2D Laplace equation. Solving the forward problem typically involves combining the equation above with a finite element model of the conductive body into a set of linear equations expressed in the form ofwhere i4(<j) is an invertible square matrix, representing a discretized expression of the complete electrode model, and I is the injected current, b is a coefficient vector that is to be solved for, which contains the elemental nodal potentials and the boundary electrode voltages.

[0138] On the other hand, the EIT inverse problem attempts to reconstruct the spatial conductivity distribution using measured boundary voltages. Solving the inverse problem generally involves minimizing the difference between the estimated boundary voltages and the actual measurements:* where a* is the estimated conductivity, 8Vgnis the estimated voltages at the boundary corresponding to a*, and 5V^easuredis the actual boundary voltage measurements.

[0139] As the EIT inverse problem is ill-posed, different optimization algorithms have been implemented to stably reconstruct the conductivity distribution. For instance, one of the most common methods is an iterative Gauss-Newton algorithm that uses the L2-norm as the regularization term, as expressed in the following equation:where J is the Jacobian matrix, 6a is the change in spatial conductivity within the medium, and 6V is the measured change in boundary voltages, a is the regularization parameter and L is the regularization matrix, often formulated as an identity matrix I. The previous equation solves for 6a by minimizing the difference between 6V and J 6a (i.e., mapped changes in the boundary voltages). The second term in the previous equation is a regularization penalty term that tackles the ill-posed nature of the EIT inverse problem and helps the solution converge. The regularization parameter a can be altered to modify the influence of the penalty term, which may be useful for processing reconstructions with noisy measurement data. The solution to the linearized regularization problem can then be obtained as6a = (JTJ + aPr dVCompressed Sensing Technique

[0140] To improve the reconstruction resolution and accuracy, another approach is based on the compressed sensing technique, which leverages the spatial sparsity of typical EIT problems.In the context of compressed sensing-based reconstruction, the objective function of the inverse problem becomes:where is the regularization parameter, and || 6cr|| is the Li-norm of do. In the previous equation, replaces a / 2 as the new hyperparameter that controls the influence of the Li- norm penalty term. The present disclosure focused on implementing the compressed sensing technique for the EIT inverse problem and adopted a two-step iterative shrinkage thresholding (TwIST) algorithm to robustly solve the previous equation. More details for the modified TwIST algorithm can be found in Wang, et al., “Development of multifunctional nanocomposite sensing systems for structural and human health monitoring”, in Structural Engineering. 2019, University of California San Diego: San Diego, California, p. 161; which is hereby incorporated by reference in its entirety herein. Both the Gauss-Newton algorithm and the compressed sensing TwIST algorithm were coupled with the designed DAQ hardware to compare their reconstruction performance.EIT Hardware

[0141] The EIT DAQ system consisted of four main components, namely, a constant current source, an array of switches / multiplexers, an analog-to-digital (ADC) converter to measure the voltages, and a controller to switch the multiplexer channels. Figure 2 shows a schematic diagram that outlines the major components of the DAQ system and their interactions. Figure 3 exhibits the physical layout of the assembled DAQ hardware, and the design of its components are described in detail below. Compared to a bundle of stationary benchtop equipment traditionally used for EIT, the proposed DAQ system’s compact footprint occupied a spatial volume of 5.33 x 15.24 x 2.54 cm3and has support for a 3.7V LiPo battery, making it portable for deployable applications. Overall, the cost of the entire DAQ hardware was estimated to be ~ 80 U.S. Dollars.

[0142] Microcontroller . An Adafruit Feather nRF52840 Express was chosen to serve as both the controller and the ADC. The nRF52840 Feather board has a small physical footprint (5.08 x 2.29 x 0.71 cm3), a built-in 2-pin Japan Solderless Terminal (JST) PH series connector that supports any 3.7V LiPo batteries, and Bluetooth Low Energy (BLE) 5.0 for wireless communication. There are also 21 general purpose input / output (GPIO) pins on the nRF52840 Feather, which were enough to support three 32-channel multiplexers in the present disclosure.

[0143] Multiplexers (MUX). The ADG732 MUX is commonly used for battery-powered systems, data acquisition systems, as well as medical instrumentation. This integrated circuit can internally connect any of its 32 channels to a common source. A total of three MUXs were utilized to perform the adjacent EIT measurement scheme. In particular, two MUXs formed the adjacent current injection pair, and the third MUX measured the voltages relative to the ground. The voltages measured relative to ground were then processed via customized code to obtain the adjacent voltage measurements. On the physical DAQ system, there was one MUX on the top and the bottom of the MUX shield, respectively, and the third was on the main printed circuit board (PCB). This interconnected architecture was designed to further minimize the footprint of the DAQ system.

[0144] Constant current source. To obtain accurate boundary voltage measurements, it is important for the EIT DAQ system to inject a controllable and constant electrical current to the medium of interest. The current source was a current mirror made of two 2N3906 bipolar PNP transistors. A 10 kQ trimmer potentiometer was used to control the reference current that was then mirrored across to the conductive material of interest. The regulated 3.3 V output from the nRF52840 was passed through an MT3608 boost converter up to 10 V to power the current source. Since the current source would only be drawing a few milliamps (6 - 20 mA out of the boost converter), the design in the present disclosure was well within the limits of the on-board 500 mA peak regulator.

[0145] Analog-to-digital converter. The built-in ADC in the nRF52840 was utilized to measure the voltages at each electrode. With 10 V powering the current source coupled by the fact the voltages were measured relative to the ground, it was inevitable that the measured voltages exceeded the allowable 3.3 V input into the ADC. To address this, a voltage divider, implemented with a 10 kQ potentiometer, scaled the measured voltages down to a maximum of 3.3 V. To ensure minimal current draw when connecting each electrode to the ADC, an OPA810 rail-to-rail op-amp, configured as a voltage follower, was placed before the voltage divider to act as a voltage buffer. The ADC resolution could be set to either 8-, 10-, 12-, or 14- bits. As is well-known, there is a tradeoff between conversion speed and resolution: higher resolution typically results in longer measurement times and vice versa. To balance the measurement resolution and speed, a 12-bit resolution ADC was utilized.

[0146] Bluetooth-based wireless communication. The nRF52840 Feather board supported the Bluetooth Low Energy (BLE) module, which enabled wireless connectivity between themicrocontroller and another Bluetooth transceiver (e.g., smartphone). The Bluefruit Connect app from Adafruit Industries was used to connect to and operate the DAQ system via the BLE Universal Asynchronous Receiver / Transmitter (UART) protocol. The UART protocol was chosen over the BLE Generic Access Profile (GAP) and the Generic Attribute Profile (GATT) protocols for compatibility with the interactive controller in the Bluefruit Connect smartphone app. FreeRTOS, a real time operating system, was used to implement cooperative multitasking allowing the DAQ hardware to simultaneously handle tasks such as Bluetooth communication and the EIT measurement scheme. It should be noted that the DAQ hardware was operated wirelessly using a smartphone to perform all the experimental measurements in the present disclosure.

[0147] EIT Measurement Scheme. The current injection method used in the present disclosure was the adjacent-current driving mode. To be specific, two adjacent electrodes were selected to be the driving electrodes, where one was used to inject the current into the material of interest and the other was grounded for current to flow out. The voltages across all adjacent electrodes were measured / recorded, and all measurements involving any of the driving electrodes were omitted. This process was then repeated for all adjacent pairs of electrodes. The total number of measurements for this driving mode can be calculated by:M = N(N - 3) where M represents the number of measurements in each measurement frame and N represents the number of electrodes. For instance, a 16-electrode setup will have a total of 208 measurements in each measurement frame.

[0148] ABAQUS simulations. There were a few uncertainties when it came to executing the measurement scheme, such as: which electrode pair starts the measurement, if measurements are taken clockwise or counterclockwise, and whether the injection electrode leads or trails the ground electrode. The prior art does not explicitly state how to perform the measurement scheme. To address these uncertainties, ABAQUS was used in conjunction with Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software (EIDORS), an open-source software package for EIT modeling, to reverse engineer the measurement frame. From EIDORS, a baseline measurement frame was taken by solving the forward problem on a homogeneous, undamaged 16-electrode domain. ABAQUS was then used to try and recreate the same measurement frame.

[0149] Measurement order. To illustrate the measurement scheme, refer to Figure 4 that shows an 8-electrode configuration as an example. Labels E0-E7 refer to electrodes 0-7, and P0-P7 refer to electrode pairs 0-7. E0 corresponds to the upper-leftmost electrode, and each electrode is positively indexed clockwise. If the sample is circular rather than quadrilateral, E0 corresponds to the topmost electrode with the rest of the electrodes indexed clockwise. The first electrode pair P0 is between E0 and El and the pairs are also positively indexed clockwise. During the measurement, current flows from El to E0 for the first injection pattern, E2 to El for the second, and so on. For each injection pattern, measurements are always taken starting with P0 (i.e., measuring the voltage drop between E0 to El) through to P7. Measurements that include any of the driving electrodes are omitted. For example, if P3 was the driving electrode pair (i.e. , current flowing from E4 to E3), the measurements would be recorded in the following order: P0, Pl, P5, P6, and P7. Measurements from P2, P3, and P4 would be omitted as they included electrodes E3 and E4. This measurement protocol also applied to other electrode configurations (e.g., 16- and 32-electrode setups).

[0150] Observed linearities and nonlinearities. While simulating EIT in ABAQUS, a linear relationship was observed between boundary voltage measurements, injection current, and base conductivity. In other words, base conductivity and injection current could be arbitrarily set and the resulting measurement frame could be linearly scaled to match other frames with other configurations (i.e., base conductivity and injection current). This makes sense since this is basically a form of Ohm’s law at play.

[0151] To further illustrate this point, the measurement frames produced from ABAQUS and EIDORS were plotted against each other. Figure 5 shows that both measurement frames are nearly identical despite significant differences in base conductivity and injection current. Minor discrepancies were present, but they were likely attributed to EIDORS being a point-electrode model and ABAQUS being a complete-electrode model. Simply put, electrodes in EIDORS were represented by a single node whereas electrodes in ABAQUS were represented by elements in the mesh. Additional configurations were also simulated, and all measurement frames lined up as shown in Figure 5 when scaled linearly.

[0152] Although there is a linear relationship between boundary voltage, base conductivity, and injection current, the relationship between anomaly conductivity and boundary voltage is non-linear. In ABAQUS, an anomaly was introduced into the sensing domain with varying conductivities and the results are shown in Figures 6A-6B.

[0153] Figure 6 shows that all measurements approach a horizontal asymptote as anomaly conductivity increases. This intuitively makes sense since there is a certain point where highly conductive anomalies all resemble a short in the sensing domain. For instance, an anomaly that is ten-thousand times the base conductivity will have a similar effect on boundary voltages as an anomaly that is one million times the base conductivity. The same can be said with decreases in conductivity.Benchmark Testing of the DAO System

[0154] Comparison with circuitry simulation. To evaluate the measurement accuracy of the designed DAQ hardware, a network of known resistors was fabricated and simulated using LTSpice, an electronic circuit simulation software. Figure 7A and Figure 7B show a diagram of the resistor network and its physical model, respectively.

[0155] To evaluate hardware performance, one electrode was connected to the current source, another electrode was connected to ground, and voltage measurements were taken across all electrodes. For example, electrode A01 was connected to the current source, electrode A32 was connected to ground, and voltages were measured from electrodes A01 through A32. As the injection and ground electrodes change, the equivalent resistance across the current source would also vary. Therefore, the performance of the current source could be tested by observing how the voltage measurements change under different loads. These voltage measurements would also be compared to those obtained from LTSpice simulation to evaluate DAQ accuracy.

[0156] Characterization of measurement noise and signal processing. Another aspect of the DAQ system performance evaluated was the level of noise in the measurements that may be induced by the ADC or current source. First, the voltage at an electrode was repeatedly measured and recorded at the highest possible sampling rate over the span of a second (z.e., approximately 500 measurements per second). The recorded values were then used to calculate the covariance and the signal -to-noise ratio.

[0157] To improve the measurement quality, a scalar Kalman filter was implemented to filter out the noise from the ADC measurements. An alternative denoising approach could be to average the recorded values for each measurement, but this is highly susceptible to noisy outliers that may heavily bias the average depending on the sample size. On the other hand, Kalman filters attempt to estimate the true state / value of the measured signal by accounting for the covariance of the original signal. In particular, the Kalman filter consisted of three steps,namely, updating the Kalman gain, updating the predicted state, and updating the estimated error. The Kalman gain can be determined with the following equation:where Ekis the estimated error in the previous timestep and R is the measurement noise covariance. The Kalman gain was then used to update the predicted state using the following equation: xk= k + Kkzk- xkwhere xxkand xk■ are the predicted current and previously predicted states, respectively. zkis the current measurement. After predicting the current state, the estimated error was updated for the next iteration using the following equation:Ek= (l - Kk) x Ek-

[0158] An additional term was added to the previous equation to account for the process variance, which represents how fast the measurements can change. The following equation expresses how the estimated error was updated:Ek= (1 - Kk) x Ek+ \xk- xk\ x Q with Q representing the process variance. When applying this filter to the DAQ system, xkwas the predicted or corrected voltage measurement and zkwas the raw measurement from the ADC.

[0159] Furthermore, the effects of Kalman filter parameters on the DAQ signals are characterized to optimize the EIT measurement speed and quality. To be specific, as the MUX channels switched for each measurement, the voltages measured by the ADC would resemble that of a step response. If the Kalman filter parameters were poorly chosen, the estimated state would exhibit a transient response with a long settling time before converging to the new state. This occurs when the Kalman filter has trouble distinguishing whether the sudden change in the measurement is due to noise or a change in the actual signal. The settling time is an important factor for EIT measurements because it significantly affects the measurement speed. For instance, 208 measurements for a 16-electrode sample will take over 20 s if each measurement takes 100 ms to settle. On the other hand, if the filter parameters were set for a fast settling time, more noise would pass the filter and corrupt the signal. Therefore, there was a tradeoff between measurement speed and quality - faster measurements were of higher noise levels and vice versa. A parametric study was conducted in the present disclosure for selectingthe optimal value for the process variance (Q) in the previous equation to achieve balanced measurement speed and signal quality.Application of the DAO System for EIT Experiments

[0160] Materials. The designed DAQ system, coupled with the EIT algorithms, was implemented to detect damage on electrically conductive materials. Here, conductive carbon- filled ultra-high molecular weight polyethylene (UHMWPE) purchased from McMaster-Carr (thickness: 0.127 mm; surface resistivity: 103Q / sq.) was used as the material of interest for the EIT experiments. To establish boundary electrodes on the conductive UHMWPE, fast-drying conductive silver paint and two-ply conductive threads were acquired from Ted Pella and Adafruit, respectively.

[0161] Sample fabrication. The UHMWPE sheets were first cut into 15 x 15 cm2squares for the 16-electrode samples. Figure 8 shows the schematic diagram of a representative edge with boundary electrodes for the 16-electrode samples. In particular, electrodes were positioned ~3.75 cm apart as close to the edge as possible. The outermost electrodes were positioned — 1.88 cm away from the adjacent edges. The boundary electrodes were established by airdrying silver paint on conductive threads for at least 30 min before testing. The contact region between each electrode and the UHMWPE sheets was ~5 mm in diameter. Furthermore, in the present disclosure, 8-electrode samples were also fabricated following similar procedures and were utilized to characterize the edge computing performance of the DAQ system. It should be noted that for the 8-electrode configuration, the UHMWPE sheets were cut into 7.5 x 7.5 cm2squares maintaining the same electrode spacing shown in Figure 8.

[0162] EIT-based damage detection experiments. To conduct the tests, the DAQ hardware was first connected to the electrodes on the UHMWPE samples using alligator clips. Then, the DAQ system was commanded wirelessly via Bluetooth to perform the EIT measurement scheme on the undamaged samples, which established baselines for the initial conductivity distribution. These baselines were compared to their theoretical values obtained from the EIT forward problem solved with the EIDORS. The forward problem model was set up as a 16- electrode system with a uniform conductivity distribution which was discretized into a 96 x 96 finite element mesh. By solving the forward problem on the model using the adjacent current driving mode, theoretical boundary voltage distributions were obtained to compare with the experimental measurements. Anomalies (z.e., damages) were then introduced in the form ofholes (~6.4 mm in diameter) cut out of the UHMWPE sheets. The holes represented regions of high impedance as no current could flow through those areas. The EIT measurement scheme was then performed again on the damaged samples to obtain a new set of boundary voltage measurements. The relative change in boundary voltage distribution, calculated by subtracting the baseline measurements, was used as input for EIT inverse algorithms for reconstructing conductivity distribution. Here, to evaluate the compatibility of the DAQ hardware with different EIT inverse algorithms, the MATLAB-based iterative Gauss-Newton algorithm and the compressed sensing TwIST algorithm were both implemented for conductivity reconstruction using the DAQ measurements. Their reconstruction resolution was quantified and compared.Edge Intelligence

[0163] To transform the traditional EIT data collection and post-processing workflow, the present disclosure further developed an edge computing functionality for the DAQ system. To be specific, the MATLAB-based compressed sensing TwIST algorithm was first simplified and converted into a C / C++ library. The re-formatted code was then further optimized to be incorporated with the DAQ system. The optimization procedures included removing redundant loops introduced from the code conversion, converting functions to be compatible with the Arduino library, and re-coding matrix multiplication to avoid storing the Jacobian matrix with on-board memory.

[0164] One of the major challenges in deploying the reconstruction algorithm was accessing the Jacobian matrix on the microcontroller, which is the largest set of data needed in the compressed sensing TwIST algorithm. The nRF52840 Feather contains 1024 kB of flash memory and 256 kB of random-access memory (RAM). Theoretically, this would be large enough to store a 208 x 1024 matrix of floating-point values corresponding to a 16-electrode setup with a 32 x 32 finite element mesh. A reasonable amount of memory allowed for storing the main program for the DAQ system. This program allowed for tasks like the EIT measurement scheme, Bluetooth communication, and TwIST algorithm to be operated simultaneously using cooperative multitasking. For this reason, the size of the Jacobian that could be used for edge computation had to be significantly reduced. In addition to the limitation of onboard memory, the lack of computational power could be another challenge. Each iteration of the TwIST algorithm would involve multiple instances of matrix multiplicationwith the Jacobian. This could be extremely demanding for a single-core microcontroller, such as the nRF52840. It should also be noted that using microcontrollers with multiple processing cores could lead to increased power consumption and reduced battery life.

[0165] Due to the hardware limitations regarding the lack of memory and computational power, the EIT sensing experiments for evaluating edge intelligence performance were simplified by reducing the number of electrodes on the UHMWPE specimens to an 8- electrode configuration. The finite element mesh was also reduced from the original 96 x 96 element mesh to an 8 x 8 element mesh, resulting in a 40 x 64 Jacobian matrix. Furthermore, rather than storing the Jacobian matrix on-board in memory, it was stored on a Secure Digital (SD) card and accessed with an external SD card reader. The available memory on the microcontroller was reserved for other large mutable arrays used in the TwIST algorithm.

[0166] Following similar test procedures described above, damages were introduced to the 8- electrode UHMWPE samples, and the corresponding relative change in boundary voltage distribution was used to perform the conductivity reconstruction on the DAQ system. The same reconstruction was also performed on a personal computer (PC) with the original TwIST algorithm as a comparison.Results and Discussion

[0167] Benchmark testing of the resistor network. The resistor network designed for benchmark testing can be simplified into an equivalent resistor between any two nodes based on the concept of series and parallel resistances. The equivalent resistance value could vary, depending on which two electrodes were chosen for measurements. For example, the equivalent resistance between electrodes A01 and A32 was -750 Q, whereas the equivalent resistance between A20 and A32 was -1200 Q. Based on this, the performance of the current source in the DAQ system could be evaluated by characterizing its behavior when subjected to various resistive loads. In addition, by applying the Kirchhoff Voltage Law to the resistor network, it was expected that the voltages at each node would be different. The voltages at each node were measured using the DAQ system and compared to their theoretical values obtained from LTSpice-based simulations.

[0168] Figure 9A shows the configuration where current was injected into A01 and out of A32. The experimental measurements, indicated by the dashed line in Figure 9C, matched closely with those from the simulation, indicated by the solid line. Switching the injection pointfrom A01 to A20, configuration shown in Figure 9B, the equivalent resistance significantly increased from ~ 750 to 1200 . The corresponding experimental results in Figure 9D also closely matched the simulated values. It was also noted that there was a slight drop in the measured voltages, approximately 4.7%, that could be caused by imperfections in circuitry and / or Joule heating. Overall, the performance of the current source was deemed sufficiently accurate and reliable.

[0169] Measurement noise and Kalman filter-based signal processing. Noise mitigation is crucially important for EIT problems due to the inverse relationship between electrode numbers and voltage differences. That is, when one wishes to achieve higher reconstruction resolution by using larger number of electrodes, the voltage differences measured across adjacent electrodes would decrease correspondingly. If the measured signals were not distinguishable from noise, the quality of the conductivity reconstruction would be significantly compromised. In the present disclosure, the noise level in DAQ measurements was quantified using the same resistor network. Figure 10 shows an example of unfiltered and filtered signals within a one- second time window, represented by the dash-dot-dash and dotted lines, respectively. The region between the outer dash-dot-dash lines and the region between the inner dashed lined highlight the unfiltered and filtered signals’ range within two standard deviations, respectively. Here, the vertical axis represents unitless digital values ranging from 0 to 4095, corresponding to a 12-bit resolution ADC. Upon converting to millivolts, the standard deviations for the unfiltered and filtered signals were 5.32 mV and 0.51 mV, respectively. In addition, it was found that the signal-to-noise ratio was increased from 66.23 dB to 86.76 dB by applying the Kalman filter, which indicated that the noise in the measured signals was effectively reduced.

[0170] In addition, the present disclosure also performed a parametric analysis for the Kalman filter to improve the potential transient response of the measured signal. First, a representative dataset was generated by adding Gaussian noise to a signal that abruptly jumped up from 350 to 400 and then back down to 300. This synthetic signal was supposed to emulate the step-like sudden changes in ADC readings as the MUXs switch channels when performing the EIT measurement scheme. Since the transient response of the filtered signal can be affected by the process variance (Q) in the previous question (z.e., the process variance increases the estimated error between the current and previous estimates), the parametric analysis was performed with process variances ranging between 0 - 2. Figure 11 illustrates representative filtered signals ofthree different Q values (z.e., 0.02, 0.20, and 2.00) overlapped with the original unfiltered dataset.

[0171] The filtered signal using Q =0.02 was found to be very clean and smooth. However, there was a notable settling time ranging between 80 - 120 ms. Here, the settling time was defined as the time it took the signal to reach 95% of its final value. On the other hand, increasing Q to 2.00 significantly reduced the settling time down to about 4 - 10 ms, but a lot of noise from the original signal passed the filter. There was a clear tradeoff between the transient performance and measurement quality - one may improve the noise attenuation at the cost of increasing the settling time. Although a settling time of a few milliseconds may seem insignificant, it can drastically slow down the measurement speed and increase the time it takes to perform the entire EIT measurement scheme. Using Q=0.02 as an example, where each measurement took an average of 100 ms to settle, for a 16-electrode setup (z.e., 208 voltage measurements), it would take over 20 s to complete the EIT measurement scheme. Instead, for a shorter settling time of 10 ms, the measurement scheme would take ~2 s to complete. Therefore, to realize an optimal balance between noise attenuation and settling time (8 - 16 ms), the Q value was chosen to be 0.20.

[0172] Furthermore, it is important to note that the aforementioned settling time also depends heavily on the ADC measurement rate. An ADC that measures twice as fast will also settle twice as fast because the number of measurements needed for convergence remains the same. For Q=0.20, it took 5 - 10 measurements for the filtered signal to settle. From an application standpoint, the EIT DAQ system would have to take at least 5 - 10 measurements before the filtered signal could be used. To be conservative, 30 ADC readings were taken for each individual measurement for all the EIT experiments in the present disclosure, where there were 20 - 25 more measurements than what was necessary for signal convergence.

[0173] Comparison between DAQ measurements and EIT forward problem simulations. The goal of this comparison is to verify whether the experimental setup using the developed DAQ system along with the conductive UHMWPE as the damage sensing material yields comparable measurements to the EIT forward problem solved with EIDORS. In Figure 12, the dashed line represents the voltage measurements from the EIT DAQ system performed on a UHMWPE sample, and the solid line represents the theoretical values calculated from the EIDORS-based forward problem on an assumed homogenous medium. It was found that the experimentalmeasurements obtained using the DAQ system were similar to the simulated voltage response, which further confirmed the measurement accuracy and reliability of the DAQ hardware. One may also observe that there were slight discrepancies between the experiment and simulation. This is likely due to potential deviations in electrode positioning and electrode contact impedance on the experimental specimens. In addition, the conductivity distribution of pristine UHMWPE samples may not be perfectly uniform as assumed in the EIT forward simulations.

[0174] Conductivity distribution reconstruction of the 16-electrode configuration. The first set of EIT damage sensing experiments was conducted on the 16- electrode UHMWPE samples. Here, damages (z.e., holes) were cut out of the material to introduce an area of high impedance at different locations (z.e., four corners) on the samples. The boundary voltage distribution was measured for each damage scenario. The relative change in voltage distribution was calculated by taking the difference between the voltage measurements from the damaged and undamaged (i.e., baseline) samples. The voltage differences were then used as inputs for the EIT reconstruction algorithms, including the iterative Gauss-Newton algorithm and the TwIST algorithm. Here, the hyperparameters in the inverse algorithms were selected based on the samples with the most anomalies in each test to achieve the optimal reconstruction of those cases. Then, the selected hyperparameters were used for the remaining reconstructions in each corresponding test. Also, more details on the hyperparameters in the EIT inverse algorithms can be found in Zhao et al., “Comparison of electrical impedance tomography inverse solver approaches for damage sensing, in Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring”, 2017, Society of Photo-Optical Instrumentation Engineers (SPIE): Portland, Oregon, United States; which is hereby incorporated by reference in its entirety herein. Figures 13A-13D and Figures 13E-13L show the images of damaged samples and their correspondingly reconstructed conductivity distributions using the two inverse algorithms, respectively.

[0175] According to the color bars, regions toward the bottom of the key in Figures 13E-13L indicate areas of decreased conductivity compared to the baseline conductivity, whereas the regions that correspond with the top of the key indicate areas of increased conductivity. It was clear that the voltage measurements of the DAQ system could be utilized for both inverse algorithms to detect damages at different locations on the specimens. The locations of reconstructed anomalies matched well with actual damages observed on the samples. In addition, to quantify and compare the performance of the two inverse algorithms, theconductivity distributions reconstructed from both were evaluated based on their pixel values. More specifically, blur radius was used to rigorously quantify the reconstruction quality and resolution. Here, the blur radius (BB) was defined aswhere d0is the total sensing area of the domain and ARis the area with significant changes in reconstructed conductivity.Rcan quantified by the following expression:where Ais the total number of elements whose conductivity values are above the threshold. The BR and dRshow that higher resolution reconstructions will lead to a smaller BR value. In other words, reconstructed anomalies with blurred features would occupy more area in the sensing domain and vice versa. The calculated blur radii of the two inverse algorithms are shown in Figure 14.

[0176] It can be observed that for all four configurations with anomalies introduced, the images reconstructed with the TwIST algorithm exhibited lower blur radii compared to those reconstructed with the Gauss-Newton algorithm. This was consistent with visual inspection of the reconstruction results (z.e., Figures 13E-13H compared to Figures 13I-13L. To summarize, the compressed sensing technique could effectively improve the accuracy and resolution of EIT reconstruction. Therefore, the remaining reconstructions performed in the EIT damage sensing experiments focused on using the compressed sensing TwIST algorithm.

[0177] Two additional sets of experiments were also conducted to further evaluate the DAQ system’s performance in detecting damage-induced conductivity changes elsewhere on the UHMWPE samples. In particular, Figure 15 and Figure 16 show the reconstructed conductivity maps corresponding to damage scenarios where multiple damages were introduced along the edges and near the central regions, respectively. While the shapes of the reconstructed anomalies did not perfectly reflect those of the damages on the UHMWPE samples, the locations of the reconstructed anomalies were found to match well. It is also worth noting that there were certain regions of increased conductivity (i. e. , the small spots toward the periphery) present in the reconstructed conductivity maps, primarily near the electrodes. Theoretically, in these EIT sensing experiments where holes were introduced to the conductivematerials, there should only be regions of decreased conductivity in the reconstructed maps. This discrepancy is likely to be attributed to artifacts from the EIT forward and inverse algorithms, where those regions of increased conductivity were computationally included to facilitate the optimization process.

[0178] Regardless, based on Figures 13A-13L, Figure 14, Figures 15A-15H, and Figure 16, one can clearly observe that the data collected from the designed DAQ system, coupled with the compressed sensing TwIST algorithm, could effectively detect damage-induced anomalous conductivity changes at various spatial locations across the sensing domain.

[0179] Edge intelligence. In the present disclosure, the edge computing functionality was incorporated with the DAQ system to transform the traditional workflow of EIT -based sensing techniques. To address the hardware limitations in memory and computational power, the EIT damage sensing experiments were conducted with fewer number of electrodes (z.e., 8-electrode sample configuration) and a coarser finite element mesh to simplify the inverse reconstruction. The damages were introduced in the same manner as outlined above. Figures 17A-17D and Figures 17E-17H show the images of a damaged UHMWPE sample and their corresponding reconstructed conductivity distributions performed using the nRF52840 Feather microcontroller in the DAQ hardware, respectively. It was found that, despite the low resolution, damages could still be detected and spatially located via performing the conductivity reconstruction on an edge device. Also, the reconstruction resolution was arguably sufficient to distinguish each anomaly apart from each other.

[0180] Several attempts have been made to improve the reconstruction resolution. First, the finite element mesh size was reduced from a 9216-element mesh down to a 64-element mesh for the sensing domain. Due to the microcontroller’s limited memory capacity, a finer mesh utilized more on-board memory for the mutable arrays and repeatedly led to crashes when performing the reconstruction algorithm. In addition, the computational power of the microcontroller further constrained the performance of EIT reconstruction algorithm. For the TwIST algorithm used in the present disclosure, it took the microcontroller about seven minutes to complete each reconstruction, and this computational time would increase exponentially with refined mesh resolution. It was found that when performing EIT reconstruction on the edge devices, the most computationally intensive task was matrix multiplication with the Jacobian matrix in the inverse algorithm. The main contributing factor was the fact that the Jacobian needed to be accessed by parsing through a CSV file on an SDcard rather than with on-board RAM or flash memory. While the additional functionalities of the DAQ system (e.g., Kalman filter-based signal processing) also uses some of the computational resources, these demands were very minor compared to performing the EIT reconstruction.

[0181] Furthermore, to demonstrate that the data collected using the DAQ system for this 8- electrode sample configuration was still of high quality, the voltage measurements were further processed using a PC (z.e., with sufficient hardware memory and computational capacity) for comparison. The same mesh size as described above was used here for the reconstruction. Figures 17I-17L show the reconstructed conductivity distributions corresponding to the multiple damages, where the detected anomalies were highly defined. The position of each anomaly also matched very well with those in the UHMWPE samples. This indicates that the data collected from the DAQ system was reliable and accurate, and the relatively low quality of reconstruction results shown in Figures 17E-17H were indeed resulted from the edge device’s computational capacity.Comparison Between a Novel Compressed Sensing-Based Neural Network and Traditional Neural Network Approaches for Electrical Impedance Tomosraphy Reconstruction

[0182] As outlined above, a smaller, faster, and more efficient reconstruction algorithm must be developed to enable low computational devices to carry out EIT reconstructions. As the field of artificial intelligence is rapidly developing, there are increasingly more platforms that enable edge devices to run machine learning algorithms (z.e., Tensorflow Lite, Edge Impulse, etc.). Artificial intelligence, especially deep learning, is a promising approach since it can address many of the aforementioned issues. A deep learning neural network can be significantly faster than traditional iterative approaches since each reconstruction is performed with a fixed number of arithmetic operations. Deep learning has also proven effective in solving nonlinear, ill-posed problems which is relevant for EIT.Electrical Impedance Tomography.

[0183] EIT consists of the forward problem and the inverse problem. The forward problem attempts to solve for the boundary voltage distribution for an assumed conductivity distribution, and the inverse problem solves for the internal conductivity distribution for the given boundary voltage distribution. In practice, the boundary voltage is measured by a data acquisition (DAQ) system and used as input for an EIT reconstruction algorithm to estimatethe internal conductivity distribution. Because different internal conductivity distributions can correspond to the same boundary voltage distribution, the EIT inverse problem is severely ill- posed and uses additional optimization techniques to aid reconstruction. One of the optimization algorithms that has been demonstrated effective is based on the compressed sensing (CS) technique, which leverages the sparsity of EIT problems to enhance the reconstruction resolution and accuracy.

[0184] A common CS algorithm used is the iterative shrinkage / thresholding (1ST) algorithm, which attempts to solve the following objective function:where 6a is the change in conductivity, J is the Jacobian for the sensing domain, 6V is the change in boundary voltage distribution between the homogeneous and inhomogeneous state, is the regularization parameter, and ||<5<J ||x, is the Li-norm of 6a. This objective function attempts to find a set of 6a that matches closely with the given 6V when transformed by Jacobian, J. The Li-norm is added to promote sparsity which greatly aids the ill-posed nature of this inverse problem. controls how much influence the Li-norm has which can help with noisy reconstructions. This objective function could be leveraged by deep learning to train a neural network.Deep Learning

[0185] Deep learning is a subset of machine learning and artificial intelligence that utilizes an artificial neural network (NN) comprised of multiple nodes that mimic neurons in a thinking brain. These nodes are organized into layers which are connected to other layers by a set of weights. Essentially, each layer in a NN is represented by a tensor, and a set of tensor operations are performed to go from one layer to another.

[0186] Deep learning includes three components: input data, expected output data, and a loss function (i.e., a metric to evaluate how well the neural network performs). During training, the NN output is compared to the expected output and evaluated using a loss function. A common loss function used for deep learning regression models is mean squared error (MSE) which can be calculated by:where ytis expected output value from the training dataset and y. is the NN output value. During training, the calculated loss is fed into an optimizer that adjusts the weights in each layer of the NN to minimize loss.

[0187] Because the goal of the optimizer is to minimize a computed numerical value, Equation(1) can be modified to serve as a loss function for NN training. In the loss function:where the NN output, <5<J, is transformed with J and compared with the NN input, SV. Note that the expected output (z.e., conductivity) is not included in the equation, which will render the training independent of the output. Rather than having the NN pickup information from patterns in the training dataset, information is picked up using the custom loss function instead. As a consequence, this approach is expected to make training more resilient to lower quality data, since the expected output in the training dataset has no effect on the calculated loss.Compressed Sensing-Based Neural Network

[0188] The proposed CS-based NN incorporates important features from the traditional 1ST algorithm, namely the architecture and the soft thresholding functions.

[0189] Architecture . The 1ST architecture for EIT can be visually represented by Figure 18. In Figure 19, the input data is mapped using the transformation matrix and it iteratively passes through shrinkage and thresholding functions until the ending criteria is met. Examples of the ending criteria can be a max number of iterations or a converging loss derived from the MSE equation. Inspired by the 1ST architecture, the novel NN developed in the present disclosure “unfolds” the iterative portion and represents each individual iteration as a separate series of layers in the NN.

[0190] Figure 19 shows the proposed CS-based NN architecture. Voltage data is first passed through a mapping layer (i.e. , a dense layer that serves as a learned Jacobian) and then branched off to compute the residual and gradient before merging back with the mapped layer. This series of operations represents one iteration of the 1ST algorithm. Thresholding was implemented through a custom activation function. Although Figure 19 only shows two iterations, the number of iterations could be further increased by continuing the pattern. Incorporating additional iterations has a negligible effect on the overall NN size, since it reuses the same sets of layers with the same weights. The model used in the present disclosure was structured to have four iterations.

[0191] Soft thresholding activation function. In addition to the Li-norm, the soft thresholding function used in 1ST also helps to promote sparsity in the output. It does so by setting values to zero if they fall within a certain threshold. The soft thresholding function can be representedwhere T is the specified threshold hyperparameter. This function yields a graph that resembles a linear profile with a dead- zone centered at zero. As mentioned previously, this thresholding function was implemented through a custom activation function. A parametric analysis was conducted using custom metrics (z.e., comparing pixel error differences in centroid position) to determine the ideal threshold.

[0192] Jacobian hyperparameter . The training method proposed in the present disclosure suggests that the artificial NN can extract information about the EIT spatial sensing domain through the Jacobian in a custom loss function. There are several factors that can affect the Jacobian, such as number of electrodes, element mesh size, and injection current. The number of electrodes and elements determine the dimensions of the Jacobian, and the stimulation injection current is directly proportional to the magnitude of each value in the Jacobian. A Jacobian was obtained from Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software (EIDORS), an open-source software package used for EIT modeling, using a stimulation amperage of 0.10 Amps. An additional hyperparameter controlled the magnitude of the Jacobian during training.

[0193] Hyperparameter tuning. Due to the nature of compressed sensing algorithms, the “loss” from each reconstruction is not a consistent metric to evaluate reconstruction quality. For example, a higher loss reconstruction may resemble the ground truth better due to increased sparsity in the output. To properly tune the hyperparameters, two custom metrics were employed that evaluate the position, size, and relative intensity of the reconstructed anomalies. The first metric is with pixel error which can be represented as:where pkand tkare Booleans that represent the pixel’s significance for the predicted pixel and the ground truth pixel, respectively. Pixels / elements are considered significant if they are a part of the anomaly. For the predicted pixel, significance is determined by:where pkis the predicted value at the corresponding pixel / element of the mesh. The ground truth pixel significance is determined by:where tkis the ground truth conductivity of the corresponding pixel / element in the mesh. Essentially, pixels / elements in the reconstruction and ground truth are binarized by significance (i.e., the element is either part of the anomaly or not) and the XOR operator was used to determine how many elements mismatch. This metric provides information regarding the reconstructed anomaly’s size and position.

[0194] The second metric is evaluating the differences in centroid position between anomalies in the ground truth and reconstruction. The horizontal and vertical centroids are calculated using:where x and y are the horizontal and vertical positions of the pixels, respectively. The difference in centroid position was then calculated with: = J(xt- xp)2+ (yt- yp)2where xtand xpare the horizontal centroids of the ground truth and predictions, respectively. yt, and ypare the vertical centroids of the ground truth and predictions, respectively. When calculating the centroids using the x and y equations above, it is important to subtract all elements by the base conductivity such that only anomalous regions have non-zero elements. This metric provides information regarding the reconstructed anomaly’s position and relative intensity.Traditional Deep Neural Network Model

[0195] Countless NN architectures have been proposed by researchers that utilize different types of layers. For comparison, two neural networks were trained using the traditional approach, including a simple fully-connected feed forward NN and a more complicated long short-term memory (LSTM) convolutional neural network (LSTMConvNet) model.

[0196] Fully-connected feed forward neural network. The simple model consists of two hidden dense layers: one with 305 nodes and one with 576. The last layer had 576 nodes to match the 24x24 output and the number of nodes in the first layer was chosen such that the total number of trainable parameters was comparable to the CS-based NN (~ 240,000 trainable parameters). This way, the efficiency of training methods can be evaluated (i.e., how much information the NN can extract for the same number of trainable parameters).

[0197] Encoder-decoder neural network model. The LSTMConvNet model utilized a combination of popular architectures that complement each other for EIT reconstructions. The model was structured in an encoder-decoder style, where an LSTM layer of four units was used to extract important features from the input data. The purpose of the LSTM was to extract positional information since the boundary voltage inputs follow a certain order. Such information is often lost when using regular dense layers. The outputs of the LSTM were then flattened and passed into a dense layer of 144 units. The 144 values from the dense layer were reshaped into a 12x 12 matrix and upscaled to the final size (i.e., a 24x24 matrix) via convolution and up- sampling layers. Convolutions were utilized to give the network spatial awareness when generating the reconstructions. The architecture diagram of the ED model can be seen in Figure 20.Training, Validation, and Testing Dataset

[0198] All datasets were generated using EIDORS where the sensing domain was modeled using a 24 x 24 element mesh in a 16- electrode configuration. Each datapoint consisted of 1-3 random anomalies which included circular, square, and rectangular anomalies of different sizes, positions, and conductivities. Examples of each anomaly are shown in Figures 21A-21D, where regions toward the lower portion of the key and regions toward the upper portion of the key represent decreased and increased conductivity, respectively.

[0199] For each anomalous scenario, the forward problem was solved to obtain the corresponding boundary voltage distribution. The relative changes in boundary voltagedistribution were then determined by subtracting the baseline voltages and normalized to the largest value in the baseline measurements to establish the training data input. The actual conductivities of the anomalous models (in units of Siemens) were saved as the expected output for the traditionally trained neural networks. A total of 10,000 data points were generated and randomly portioned into a 70 / 20 / 10 split for training, validation, and testing. White gaussian noise was also added to all datapoints such that the signal-to-noise ratio of the input data was ~45 dB.

[0200] Two sets of validation data were generated: one set with only one anomaly present and the other with 1-3 anomalies, similar to the training dataset. The single anomaly dataset was used for hyperparameter tuning and the multiple anomaly dataset was used to monitor / track training losses. Two validation datasets were needed because the custom metrics mentioned previously can only be used to evaluate both types of NNs if one anomaly is present. For example, if a reconstruction contained two anomalies with different conductivities, one of 15 Siemens and the other 50 Siemens, it is possible for the 15 Siemens anomaly to be deemed as insignificant since the threshold is set with the larger 50 Siemens anomaly. In addition, both types of NNs, traditionally trained and CS-based, have different outputs. The traditionally trained NNs output actual conductivity whereas the CS-based NN outputs changes in conductivities. These discrepancies can be accounted for only if one anomaly is present in the reconstructions.

[0201] There were also two sets of testing data for the same reason mentioned previously. After NN training, the testing dataset were used to evaluate differences in loss, blur radius, and centroid position, which would provide insight into the actual performance of each NN. Compressed Sensing-Based Neural Network Training

[0202] The compressed sensing-based NN was trained with a IE-4 learning rate and the Adams optimizer. With the single anomaly validation dataset, multiple training sessions were carried out to determine the optimal set of hyperparameters. For each trial, the NN was set to train for an excessive number of epochs until all metrics stabilized which helped to determine when to end the training. After identifying the optimal set of hyperparameters, training was repeated with the multiple anomaly dataset and the losses were tracked to identify potential signs of overfitting.

[0203] Hyperparameter tuning. Using the single anomaly validation dataset, the metrics were tracked and plotted for all training epochs. Figure 22 and Figure 23 show how pixel error and A centroid changed over epochs, respectively.

[0204] First, one can observe from Figure 22 that reconstructions had the smallest pixel error when k = 0.0010. Slightly increasing or decreasing by 0.0002 resulted in higher pixel error. Figure 23 shows that for all ’s, there is a bit of instability with the A centroid metric for the first 1250 epochs. It should be noted that other values ranging from 0.0001-0.0100 were also tested, but the differences in anomaly centroids were noticeably higher and more unstable (excluded from graph for clarity). To achieve a good balance between pixel error and A centroid, a X of 0.0010 was determined to be the optimal hyperparameter. The same process was repeated for other hyperparameters in the NN, such as T from the soft thresholding activation layer. Based on the results shown in Figure 22 and Figure 23, all metrics appear to remain stabilize after -1400 epochs which indicated a good stopping point to end the training.

[0205] Training losses. Figures 24A-24B is a plot that tracks how the average batch loss changes over epochs for both training and validation. It was observed from Figure 24A that the validation loss (dash-dash line) nearly matched the training loss (solid line) for all epochs during training. This suggested that the NN would exhibit similar performance and behaviors when presented with new data it has not seen before. Typically, with traditionally trained NNs, a diverging line is present between training and validation loss which signifies overfitting since newly extracted features only apply to the training set. Since the NN is trained to minimize an objective function, as opposed to directly matching the output to a finite set of data, this trend of matching losses was expected.Traditional Neural Network Training

[0206] For both the simple dense model and the LSTMConvNet model, training was carried out with the Means Squared Error (MSE) loss function along with a IE-3 learning rate and the Adams optimizer. The dense layer in the LSTMConvNet used an L2regularization with a factor of 0.005 to minimize overfitting. Note that other factors were also tested, but 0.005 appeared to work best. The L2regularization penalized larger weights and thus encouraged a simpler model that generalized and created clearer reconstructions. Furthermore, the decoder part of the LSTMConvNet utilized Batch Normalization after each convolution, which standardized the inputs to a layer for each mini batch. This helps the neural network learn more efficiently,often needing fewer epochs. It also helps to prevent the model from relying too much on specific features, which can reduce the necessity for implementing other techniques to prevent overfitting (e.g., dropout).

[0207] As seen in Figures 25A-25B, the training and validation losses begin to diverge after -170 epochs. The validation loss plateaued and remained mostly stationary while training loss continued to decrease steadily. This makes intuitive sense, since the model depends ontheMSE loss function which fits to the training data. Training was terminated after 1200 epochs because there was no more improvement with either the training or validation loss.

[0208] Loss and Metrics. The training losses and metrics are summarized in Table 1. For the traditionally trained neural networks (i.e., trained with MSE), validation and testing losses are noticeable greater than the training loss. As mentioned previously, this indicated overfitting, since the NN is extracting information and patterns only present in the training dataset. However, with the CS- based NN, this is not the case. In fact, the loss computed from the testing dataset shows even lower losses compared to training loss. This is likely the case because patterns are extracted from the custom loss function, not the data.

[0209] From the results tabulated in Table 1, it is predicted that reconstructions from the CS- based NN will accurately position the anomaly with good relative intensity, as indicated by the low ACentroid. However, there will likely be discrepancies in the sizes of the reconstructed anomalies as indicated by the larger pixel error. With the ED model, it is predicted to accurately match the sizes of anomalies, indicated by low MSE loss and pixel error, but there may be discrepancies regarding the relative intensity of reconstructed anomalies. In other words, the overall size of the anomalies will likely match, but pixels / elements of great intensity may appear scattered or concentrated in specific regions inconsistent with the ground truth.TABLE 1. PERFORMANCE METRICS FOR ALL NEURAL NETWORKS AFTER TRAINING.* - Evaluated w / custom loss function** - Evaluated w / Mean Squared Error loss functionReconstruction Results

[0210] Simulated data. To evaluate the performance of all reconstruction algorithms, a representative dataset was generated, and noise was added to achieve a more reasonable signal- to-noise (SNR) ratio of - 86 dB. The reconstruction results from all algorithms are shown in Figure 26.

[0211] The traditional 1ST algorithm was set for 5000 iterations with a of 0.001 (z.e., the same A used in the CS-based NN). Minor artifacts were present and scattered throughout the reconstruction, which were primarily due to the noise added. Using noise free voltage measurements from the same set of ground truth scenarios showed little to no artifacts (results are not shown here to better justify the comparison).

[0212] The simple, fully-connected, feed-forward NN did a decent job generalizing the patterns for EIT reconstructions, but the outputs lacked sparsity. In other words, one may still be able to identify the anomalies, but the reconstruction resolution was quite low. Outputs from this NN resembled traditional 1ST reconstructions with T set too low. Significantly more artifacts were present compared to traditional 1ST.

[0213] The LSTM’s and convolution layers in the LSTMConvNet model were able to extract more patterns in the voltage measurements, leading to clearer reconstructions. It should be noted that it was able to do so while having nearly half of the trainable parameters (-125k). This suggested that LSTM’s and convolution layers are much more effective and efficient at identifying features / patterns crucial for EIT reconstruction compared to dense layers. As indicated by the low MSE error, this NN did an effective job matching the output to the supposed ground truth.

[0214] Compared to traditional 1ST, the CS-based NN showed arguably better denoising performance, as less artifacts were present in the reconstructions. Given that this was never exposed to the expected outputs in the dataset, these results show that it is possible to train aNN for EIT reconstructions using the CS objective function as a loss function. An additional benefit to using a CS-based NN over the traditional 1ST algorithm is reconstruction speed. Traditional 1ST took ~ 0.57 s for each reconstruction (using MATLAB), whereas the CS-based NN took ~ 0.053 s (using Python). Considering differences in programming languages, the stated times are not a perfect comparison, but the NN was still an order of magnitude faster.

[0215] Experimental Data. Previously, the performances of all NNs have been evaluated with simulated data from EIDORS. The performances shown in Figure 26 are not necessarily representative of how they would perform with experimental data collected by a data acquisition (DAQ) system. All reconstruction algorithms were evaluated using experimental data previously gathered with a wireless, portable DAQ system developed by the authors. Electrically conductive ultra-high molecular weight polyethylene (LTHMWPE) was used as the sensing material and holes were cut to introduce regions of high impedance. The reconstructed results are shown in Figure 27.

[0216] There are significantly more factors at play that make reconstructing experimental data challenging. For example, there could be slight discrepancies in electrode spacing and imperfections within the sensing domain that leads to data exhibiting patterns not representable by white Gaussian noise. Based on Case 1 in Figure 10, both the traditional 1ST and CS-based NN were able to reconstruct the four anomalies in the corners of the LTHMWPE. The simple dense network struggled to capture the bottom right anomaly. The LSTMConvNet was able to slightly identify regions of decreased conductivity in the corners, but the overall reconstruction was dominated by a supposed anomaly in the left-center of the sensing domain. However, Case 2 was challenging for all NNs. There was still some resemblance between the traditional 1ST and CS-based NN. All NNs performed reasonably well for Case 3. The simple dense and CS-based NNs had comparable results to traditional 1ST and the ground truth. The LSTMConvNet was also able to capture the three anomalies, but there were some discrepancies with the anomalies’ relative intensity. Results from Figure 27 show that good performance with simulated data does not necessarily translate into good performance with experimental data, which is especially true for traditional NNs that heavily rely on the training data.

[0217] Implications. The results from Figure 24A, Figure 24B, Figure 25A, Figure 25B, Figure 26, and Figure 27 suggest that the unconventionally trained CS-based NN was successful in extracting information from the sensing domain through the Jacobian in the custom loss function. The CS-based NN was able to achieve similar performances comparedto the traditional 1ST while being an order of magnitude faster. It was also more robust compared to traditionally trained NNs as evident by the reconstructions with experimental data. There are, of course, drawbacks to this unconventional training methodology. The sizes of reconstructed anomalies often appear larger than the ground truth which is where the LSTMConvNet tends to perform well. An interesting NN architecture to test would be a combination of the CS-based NN with the LSTMConvNet. For example, the CS-based NN would be used to generalize the sensing domain convolutional / upscaling layers could be used to further refine the reconstruction. The loss function would be the weighted sum from the MSE and loss equations above. This way, the resulting NN has the advantage of extracting patterns from the Jacobian, and the reconstruction resolution and quality can be improved via MSE loss. Conclusions

[0218] The present disclosure shows that aspects from the compressed sensing technique can be leveraged by deep learning to strategically train a neural network for EIT reconstructions. The CS-based NN shares features from compressed sensing, most notably the activation functions, objective / loss function, and the architecture. Two traditionally trained NNs (z.e., trained with the commonly used MSE loss function) of varying complexity served as baselines for comparison. Sets of training, validation, and training data were generated via EIDORS. The hyperparameters in the CS-based NN were tuned using two custom metrics that evaluated the size, position, and relative intensity of reconstructed anomalies. Results show that the CS-based NN successfully extract patterns from the custom loss function rather than the training data. When trained with the custom loss function, the resulting NN exhibited similar performance with new data (i.e., achieved similar metrics with the testing dataset). This is usually not the case with traditionally trained NN as indicated by the differences in loss between training, validation, and testing data. The LSTMConvNet showed that LSTMs and convolutional layers were much more efficient in extracting patterns for EIT. Future research should consider combining the CS-based NN architecture with upscaling convolutional layers. The resulting NN could then extract patterns and information regarding the sensing domain through the Jacobian and the reconstruction resolution could be refined by means of convolutional layers and MSE loss.Carbon Fiber Reinforced Polymer

[0219] The present disclosure outlined EIT experiments conducted with UHMWPE as the sensing material. The present disclosure assesses the feasibility of using carbon fiber composites as the sensing material. Because there are significantly more engineering applications with carbon fiber, the ability to spatially locate damage in composite structures can be beneficial.Carbon Fiber Reinforced Polymer

[0220] Carbon fiber reinforced polymers (CFRP) are a highly sought after engineering material for their high strength-to-weight ratio. CFRPs allow for significant mass reduction in automotive and space applications. The carbon fibers provide strength and stiffness while the polymer matrix holds the fibers together and provides toughness. Since the strands of carbon fiber are electrically conductive, it is possible that a matrix of carbon fibers could produce a conductive medium viable for EIT. With the prevalence of CFRP in engineering structures such as aircraft wings, tails, and fuselages, spatial damage detection could be extremely important for diagnosing and preventing structural failures.EIT Conductivity

[0221] The first concern with using CFRP as an EIT sensing material is the insulating epoxy matrix that surrounds the carbon fibers. Conductivity tests were performed on generic CFRP plates purchased from Amazon. If EIT can be performed on commercially available CFRP, it would demonstrate the compatibility of EIT with existing CFRP structures.

[0222] To assess conductivity, regions of silver paint were air dried on both the surface and sides of CFRP, forming electrodes. A Keysight 34465A Digital Multimeter was used to measure the resistance between electrodes. Figure 28 shows the CFRP test sample.

[0223] The resistance between two surface electrodes ranged from 180 - 350 Q whereas the resistance between two edge electrodes ranged from 1 - 10 Q. The cut edges have exposed carbon fibers allowing current to directly flow across, resulting in an extremely low resistance. For surface electrodes, electrical current must pass through the thin layer of polymer before reaching the conductive fibers, resulting in higher resistance. The resistance measured between surface and edge electrodes is ~ 150 Q, suggesting that the polymer matrix has an effect on conductivity. For EIT specifically, the increased resistance is actually beneficial since less current is needed to achieve measurable voltage differences across neighboring electrodes.EIT Compatibility

[0224] While the previous section suggests that CFRP is conductive, the next concern is whether CFRP is compatible with EIT. When it comes to EIT reconstructions, the conductivity distribution is often assumed to be homogeneous and electrically isotropic. Given the anisotropic nature of CFRP (depending on the weave pattern), it is possible that the measured boundary voltage distribution is incompatible with the reconstruction model.

[0225] Materials and equipment. A 75 mm square piece of CFRP was configured as an 8- electrode sample following procedures previously described. A benchtop Siglent SPD3303X- E Programmable DC Power Supply was used to output a constant injection current of 30 mA and a Keysight 34465 A Digital Multimeter was used to manually measure the boundary voltage distribution.

[0226] While taking the baseline measurements, it was observed that voltages measured relative to “ground” fluctuated significantly compared to those taken across adjacent electrodes. In other words, voltages at each electrode heavily fluctuated when measured with respect to the negative terminal in the current source. Directly measuring the adjacent voltages resulted in cleaner and more stable measurements. This would suggest that the 3-MUX architecture in the previously developed DAQ is incompatible with CFRP.

[0227] Induced structural damages and reconstructions. Several damage cases were tested: drilled through holes, partially drilled holes, drilled slots, and hammer blows. The drilled through holes create regions of high impedance as current could no longer flow through that region. Similar logic applied to the slotted holes. The partially drilled holes also disrupt conductivity, but the overall effect should be less than that of the fully drilled through-holes. Hammer blows were predicted to fracture the polymer matrix, reducing the internal fiber-to- fiber conductivity. The EIT measurement scheme was manually performed on the damaged samples, and the resulting changes in boundary voltage distribution were inputted into the TwIST algorithm for reconstruction.

[0228] Figure 30 shows that it is possible to spatially locate each individual damage and the reconstructions also resemble those from Figures 17A-17H. Figure 31A shows some discrepancy between the CFRP sample and the reconstruction. There are several factors that could have led to this: lack of reconstruction resolution using 8 electrodes, anisotropic inconsistencies, and / or unintentional damage to electrodes while creating the slot. The same sample in Figure 31A was also used to test reconstructions for the partially drilled holes, asshown in Figure 32. Rather than using the undamaged measurement frame as the baseline, the damaged sample with the slotted hole served as the new baseline to evaluate subsequent damages.

[0229] Despite using the damaged measurement frame as the baseline, it was still possible to isolate subsequent damages. As expected, the partially drilled holes resulted in less intense reconstructions compared to the drilled through holes in Figures 30A-30H.

[0230] Results from the induced hammer impact damage are shown in Figures 33A-33H. The reconstructions suggest that it is possible to spatially locate impact damages in CFRP. Subsequent impacts to the CFRP appeared to intensify previously induced damages. It is likely that the shock from subsequent impacts, occurring possibly in different regions, exacerbates existing damage to the already compromised polymer matrix, leading to the observed outcome. ABAQUS Simulation Results

[0231] A similar damage scenario from Figure 31A was recreated in ABAQUS to verify whether the lack of sensing resolution with 8-electrodes was the issue. In the simulation, two types of slots were introduced: a representative slot and a simplified slot. This was done since the physical geometry of the slot would likely influence the reconstruction.

[0232] Reconstructions from the ABAQUS model show that it is possible to spatially locate the slotted hole, but the resulting reconstructions all have rounded features inconsistent with the damage. The rounded features are likely attributed to the ill-posed nature of EIT reconstructions. As expected, the 16-electrode reconstructions are of higher resolution compared to those from the 8-electrode simulations.

[0233] Across all ABAQUS simulations, it was not possible to recreate the results from Figure 31B. It is likely that there was unintentional damage to the upper left electrode while the slotted hole was created.Conclusion

[0234] Preliminary tests performed on the CFRP show that, for the most part, it is compatible with EIT. Fluctuation in voltage measurements when measured relative to “ground” indicated that the developed DAQ system is incompatible with CFRP. It is also possible that these fluctuations were worsened by having a relatively conductive material in combination with a high injection current. Another DAQ system must be developed to support adjacent voltage measurements for compatibility with CFRP.EIT Hardware - Second Design

[0235] The developed DAQ system could not support CFRP as a sensing material due to its hardware architecture. When measured relative to ground (z.e., the negative junction in the current source), voltages heavily fluctuated to the point where measurements were unusable. A second design, as described below, of an EIT DAQ system supports CFRP.EIT Hardware

[0236] Since the DAQ needed to be redesigned, this was an opportunity to introduce additional features such as alternating current (AC) injection mode. AC is often used for EIT when it comes to imaging biological tissue. There is a range of frequencies where bioimpedance is lowest due to its inherent capacitive characteristics.

[0237] Microcontroller . With the implementation of deep learning in mind, it was crucial to find a microcontroller with sufficient memory to store the neural network. The same nRF52840 microcontroller was chosen since it had a great balance between size, number of GPIO pins, onboard memory, and wireless functionality with Bluetooth communication.

[0238] Multiplexers (MUX). For measuring the voltage difference between electrodes, the previous 3-MUX architecture must be changed to a 4-MUX architecture: two for current to flow in and out, and two for measuring voltage differences. To support having 4 MUXs, the number of electrodes was reduced from 32 to 16 which actually increases the number of GPIO pins from 15 (3 MUXs x 5 digital pins for 25channels) to 16 (4 MUXs x 4 digital pins for 24channels). The ADG706 was chosen for its low ON resistance and low power consumption.

[0239] Constant current source. To facilitate two both types of current injection (e.g., AC and DC), a voltage-to- current converter (VCC) was chosen. The diagram of the VCC is shown in Figure 35.

[0240] Under ideal op-amp assumptions, V+is equal to V_ . Therefore, the current flowing across Rt>iasto ground is determined by . Since current entering the op-amp from V_ is bias assumed to be zero, applying Kirchhoff s Current Law shows that the same current flows across Rbias and Rioad-canbe controlled by the nRF52840, via low-pass filtering pulse width modulated (PWM) signals.

[0241] For constant current with AC, the same circuit can be used with a sine wave as the reference voltage. An AD5933 was used as a programmable signal generator and a high pass filter was used to remove any DC offsets.

[0242] Instrumentation amplifier + precision rectifier. To amplify the voltage differences across the electrodes, the INA188 instrumentation amplifier was used. An external resistor could be placed between pins on the chip to control the gain. Since the goal is to support both AC and DC measurements, it was crucial to rectify AC signals such that it can be measured by the ADC on the nRF52840. A precision rectifier was designed for this application and the schematic is shown in Figure 36.

[0243] Because the rectifier op-amp operates between ±5V, an additional op-amp configured as a voltage follower served as a buffer to protect the onboard ADC by limiting the output voltages to 3.3V.

[0244] Power rails. To facilitate both the AC current source and precision rectifier, it was necessary to have both positive and negative power rails. A PDSE1-S3-D5 DC-DC converter was used to convert the regulated 3.3 V output from the nRF52840 into ±5 V. These power rails enabled the voltage-to-current converter to output AC with zero DC offset and allowed the precision rectifier to handle AC signals.Benchmark Testing

[0245] Constant current source performance. To evaluate the DC current source performance, the current source was programmed to output various currents: 0.1, 0.2, and 1.0 mA. Known resistances were placed across the current source and the voltage across the load was measured. According to Ohm’s law, as the resistance load increases, the voltage across the load should increase proportionally for the same current.

[0246] Figure 37 shows a plot that compares the voltage across load as a function of resistance load across the current source. A linear trend can be observed, indicating that the current source could maintain the same output current despite being subjected to various loads.

[0247] The performance of the AC current source was also tested in a similar manner, but Root Mean Squared (RMS) voltage was measured instead.

[0248] Looking at Figure 38, the same linear trend was observed. Again, this indicated that the constant current source can maintain the same current under various loads.

[0249] Instrumentational amplifier performance. To evaluate the measurement circuitry, known voltages were placed across the INA188 inputs and the ADC readings were measured / recorded. Known voltages were supplied by a Siglent SPD3303X-E ProgrammableDC Power Supply. Voltages were verified via a Keysight 34465A Digital Multimeter and compared with ADC readings. Results from this benchmark test are shown in Figure 39.

[0250] The instrumentation amplifier was configured for a gain of 1000, but the observed gain was closer to -625. The reason behind this is likely due to how gain is calculated: G = 1 +There is only about a 50 1 difference between a gain of 500 and 1000 compared to a 37.5 RG kfl difference between a gain of 2 and 5. Factors like resistor tolerances and circuitry imperfections may have led to the observed inconsistencies.

[0251] Despite the discrepancies in gain, the measurement circuitry should work fine. The actual magnitude of measured voltage is not important, but rather the relative changes in voltage between damage scenarios. In other words, precision is key for EIT measurements, not accuracy.

[0252] Additional observations include a spike in measured voltages between ±1 mV. With all precision rectifiers, there are limits to its operating range, and it appears that the lower bound threshold is located at approximately ±1 mV. Regarding the rest of the behavior, the circuit worked as expected where both positive and negative voltages can be rectified relatively linearly within operating voltages.CFRP EIT Experiments

[0253] Materials. Generic 1 mm thick CFRP plates with the twill weave pattern were purchased from Amazon. The electrodes were strips of copper tape (1 / 8” wide) also purchased from Amazon. Fast-drying conductive silver paint was purchased from Ted Pella.

[0254] CFRP sample fabrication. The CFRP plates were first cut into squares - 100 mm squares using a tile saw. Stripes of copper tape were cut and positioned onto the CFRP samples in a configuration to ensure proper connection. Silver paint was air-dried over the copper electrodes, ensuring sufficient contact between the copper and CFRP surface. Both 8- and 16- electrode test samples were fabricated. Copper tape was chosen over the conductive threads as they were significantly easier to work and resulted in lower electrode impedances.

[0255] 8-Electrode EIT Tests. The CFRP samples were connected to the DAQ system via alligator clips. For the initial test, the DAQ was programmed to output 40 mA of current. Since CFRP is relatively conducive compared to other materials tested in the past, a high injection current was needed to achieve measurable voltage differences across the electrodes. With the DAQ set up, it was commanded wirelessly to carry out the measurement scheme to record aseries of baseline measurements. Figure 40 shows the boundary voltage distribution compared to theoretical voltage measurements from EIDORS when scaled to similar magnitudes.

[0256] Figure 40 shows high similarity between the boundary voltage measurements on the 8- electrode CFRP and the theoretical simulations. As expected, there were slight discrepancies which were likely attributable to imperfections in electrode spacing and / or non-homogenous conductivity distribution in the sensing domain.

[0257] A 7 mm drill bit was used to induce areas of increased impedance into the sensing domain. The results from the 8-electrode CFRP test are shown in Figures 41A-41H. Figures 41A-41H shows very clean reconstructions with little to no noise or artifacts. These results suggest that the new DAQ system is compatible with CFRP, at least for the 8- electrode configuration. To evaluate the DAQ’s sensitivity to changes in the sensing domain, an additional 8-electrode sample was fabricated to compare how measurements differ between partially and fully drilled holes. Theoretically, the partially drilled holes still allow for some current to flow through the affected region, so the overall change in conductivity is less compared to a fully drilled hole. Figure 42 shows a plot that compares the relative changes in boundary voltage between a partially and fully drilled hole in the same region.

[0258] The overall shape of the voltage distribution remains mostly the same, but the magnitude of each relative change is generally greater with the fully drilled hole. With the same set of hyperparameters, Figure 43 shows how the reconstructed anomalies compare. As expected, the reconstruction for the partially drilled hole is of less intensity compared to that of the fully drilled hole. Results from Figure 40 - Figure 43 attest to the DAQ’s performance and measurement quality.

[0259] 16-Electrode EIT Tests (Holes). The same test was repeated with partially drilled holes on a 16-electrode sample. With 16-electrodes, the voltage differences across adjacent electrodes are much smaller, making measurements more susceptible to disturbances that can affect measurement and reconstruction quality. Coupled with the subtle conductivity changes caused by the partially drilled holes (see Figure 42), this will fully test the capabilities of the redesigned DAQ system. In a similar manner to before, the baseline measurements were plotted against theoretical simulations from EIDORS, results shown in Figure 44.

[0260] There were strong resemblances between the experimental measurements and the theoretical simulations. Compared to the measurements taken from the previous DAQ (see Figure 12), these measurements matched much closer to simulation results.

[0261] Figures 45A-45H shows reconstructions corresponding to the damages induced to the CFRP. There were a few artifacts present, especially in the first damage scenario, but the reconstructions were still able to spatially locate regions of decreased conductivity corresponding to the partially drilled holes.

[0262] 16-Electrode EIT Tests (Impact + Slot). So far, all tests have been performed using drilled holes as the damage which is not realistic to what CFRP will likely be subjected to. An additional set of tests have been conducted to see if EIT can spatially locate damages induced by blunt impact. To induce the damages, a ball-peen hammer was used to strike the CFRP.

[0263] Results from Figures 46A-46H show that EIT reconstructions using measurements from the new DAQ system were able to spatially locate where the hammer struck the sample. When the CFRP is struck, the blunt impact disrupts the polymer matrix, effectively lowering the fiber-to-fiber connectivity within the sample. This likely explains why the reconstructed damages show up as decreased in conductivity rather than increases. Figure 47 shows the underside of the struck CFRP sample (z.e., side opposite to where the impact took place). Fractures in the polymer matrix are clearly visible and they propagated through the thickness of the material.

[0264] A cold chisel was used to introduce slotted damage into the CFRP samples. Hammer strikes were also introduced to observe how subsequent impacts affect existing damage. In Figures 48A-48H, some discrepancies were present between the slotted damage and the reconstructions. Upon closer inspection, material was still present in the chiseled slot. This likely explains why the reconstructions were not as severe as those shown in Figure 34. Regardless, the location of the reconstructed damage correlates well with the induced damage. Subsequent hammer blows were also detectable, evident by regions that correspond with the bottom of the key intensifying near the affected regions.Conclusion

[0265] The second iteration of the EIT DAQ system was redesigned to support adjacent voltage measurements by using a 4 MUX architecture as opposed to the 3 MUX architecture in the previous iteration. To test the DAQ’s precision and sensitivity to subtle changes in the boundary voltage, partial holes were drilled into 16-electrode CFRP samples. Despite the subtleties, results show that measurements from the DAQ could be used to reconstruct all damages. Additional tests were performed on CFRP samples subjected to various impactdamages. Again, results show that the corresponding measurements could be used to spatially locate all induced impact damages.

[0266] Several unsuccessful attempts were made to utilize EIT with AC injection. There were a significant number of factors at play that may have affected this. Just to name one, the precision rectifier was designed to rectify AC signals in the order of 10s of kHz. However, the INA188 instrumentation amplifier had a varying operating bandwidth that changes with gain. At the highest gain, the operating bandwidth is ~1.5 kHz which is a magnitude lower than what the precision rectifier was designed for. It is important to note that the INA188 had one of the highest operating bandwidths for a zero-drift, rail-to-rail instrumentation amplifier at the time of the present disclosure. This should be addressed in future research.CS-Based Neural Network with CFRP and Edge Intelligence

[0267] The present disclosure outlines the compatibility between the new DAQ system, CFRP, and CS-based NN. Following is a discussion of challenges encountered when attempting to deploy neural networks onto edge devices.CFRP and Compressed Sensing-Based Neural Network

[0268] Figures 49A-49H, Figures 50A-50F, and Figures 51A-51G show the CS-based NN reconstructions performed using experimentally collected from the 16-electrode EIT tests. In Figures 49A-49H, the damages are very clear in the reconstructions, and they spatially align with their respective anomalies.

[0269] The NN struggled to reconstruct the damage corresponding to Figure 50A. It appeared that the changes in boundary voltage were far too subtle for the preset regularization hyperparameters. This behavior is consistent with traditional iterative reconstruction algorithms (z.e., reconstructions come out blank if the hyperparameters are not properly set). Lowering the T threshold and adjusting other hyperparameters could enable the NN to detect the damage, but it could also jeopardize reconstruction quality with other damage scenarios. Damages from Figure 50B and Figure 50C were severe enough to be reconstructed and spatially located by the NN.

[0270] Judging from the results in Figures 48A-48H, it was no surprise that the NN struggled to reconstruct the chisel damages. Both the chiseled slots could be spatially located with the CS-based NN, but there were also a significant number of artifacts present. Looking at the overall performance from Figures 49A-49H, Figures 50A-50F, and Figures 51A-51G, theCS-based NN appeared to be compatible with CFRP and able to spatially locate most induced damages.

[0271] Deployment of Neural Network. The initial goal was to deploy the CS-based NN onto the microcontroller, enabling the EIT hardware to perform reconstruction onboard without relying on an external computer. However, several obstacles arose when it came to deployment. The TensorFlow model must first be quantized into either integers or 16-bit floats as opposed to the default 32-bit floats. This is done to reduce model size and improve CPU performance on edge devices. The quantized model would then be retrained before exporting as a TensorFlow Lite model. However, due to the custom layers, activation functions, and overall NN architecture, quantization is rather challenging. To successfully quantize the model, it would involve diving extremely deep into the low-level programming with the TensorFlow and Keras framework. This was slightly outside the intended scope of the present disclosure.

[0272] Despite not having a fully quantized model, a comparatively inefficient TensorFlow Lite model could still be exported. Edge Impulse was the platform of choice for converting the tflite model into a compatible Arduino or C / C++ library. When uploading the Arduino library, it was discovered that the exported library was not compatible with the Adafruit Feather nRF52840 Express. Previous attempts were successful in uploading deep learning algorithms onto an Arduino Nano 33 BLE which used the same microcontroller chip. It was assumed that if a deep learning algorithm could successfully deploy onto the Arduino Nano 33 BLE, there should be no problem uploading the algorithm onto the Adafruit nRF52840. In hindsight, this should have been verified much earlier in development.

[0273] The same Arduino library was deployed onto a Sony Spresense to see if inferencing with a microcontroller was even possible to begin with. It was found that the unquantized model was still too large for the Spresense. Runtime errors indicate issues with memory addresses, likely trying to allocate more memory than what is available. Note that the Spresense has more on-board memory compared to the nRF52840 (8MB flash and 1.5MB RAM verses 1MB flash and 256kB RAM, respectively). Therefore, even if the Arduino library was compatible with the nRF52840, issues with a lack of memory persist. To properly address this issue, model quantization is non-negotiable and should be addressed in future research.

[0274] Although Edge Impulse does provide end-to-end NN development along with model quantization (if the NN is trained through their workflow), there is not much support for custom architectures like the one developed for EIT. One possible direction could be to implementalternative forms of edge intelligence, not necessarily EIT reconstructions. For example, a NN could be trained to classify whether an anomaly is present in the sensing domain. This could still be technically considered as a form of edge intelligence.First Example of Electrical Impedance Tomography Data Acquisition System with Deep Learning Edge Computing Functionality

[0275] The present disclosure serves as a steppingstone towards developing the next generation of smarter, standalone EIT DAQ systems capable of performing analysis (z.e., classification, image reconstruction, etc.) efficiently on low-powered edge devices. Two iterations of EIT DAQ system have been developed that have both shown success spatially locating damages with their own respective sensing materials.

[0276] First iteration of DAQ system. The first iteration of the DAQ was able to spatially locate holes cut into conductive UHMWPE. A modified TwIST algorithm was deployed onto the system to perform on-board image reconstructions using a course element mesh. In conjunction with preliminary tests performed on CFRP, several issues arose regarding the efficiency of deployed reconstruction algorithms as well as issues with the DAQ architecture. An efficient reconstruction algorithm was needed if deployment onto edge devices was the end goal, and a redesign of the hardware was also necessary to facilitate additional sensing materials (e.g., CFRP).

[0277] Compressed sensing-based neural network. By leveraging the objective function in the compressed sensing technique, a custom loss function was formulated to strategically train a NN. With this unconventional approach, information regarding the sensing domain was extracted from the Jacobian in the loss function rather than the data. NN performance was consistent across training, validation, and testing datasets with little to no evidence of overfitting. This is primarily due to loss being computed via objective function rather than MSE. The proposed NN could achieve comparable results to traditional iterative algorithms while taking a fraction of the time. In the presence of experimental data, the proposed algorithm proved its robustness by successfully identifying patterns where other NN architectures struggled.

[0278] DAQ redesign for second iteration. The second iteration of the first example of the DAQ system utilized a 4 MUX architecture that supported adjacent voltage measurements. EIT experiments showed that the DAQ was compatible with CFRP, and the correspondingmeasurements could be used to spatially locate all damages. Reconstruction results shown in the 16-electrode EIT tests attest to the DAQ’s precision and sensitivity to extremely subtle changes in boundary voltage. With data collected from the new DAQ system, the CS-based NN was evaluated, and it too was able to spatially locate most anomalies corresponding to the induced damages.

[0279] AC and DC operation. Supporting both AC and DC EIT measurements using shared circuitry is possible, but said AC and DC DAQ systems are ideally developed and constructed independently. In the DC system, there is no need for the precision rectifier, so the resulting system could be simpler and potentially even higher performance without unnecessary circuitry. To amplify the voltages for measurements, a multistage instrumentation amplifier could be used over a single instrumentation amplifier to further increase the gain. A digital potentiometer could also be implemented to control the gain via software to improve user experience.

[0280] For the AC system, signal rectification may not be the best solution. With the extremely high gains needed to amplify boundary voltages, instrumentation amplifiers have a relatively low operating bandwidth, often outside of the desired frequency. Alternative approaches involve either implementing impedance analyzers or signal demodulators. Both utilize an integrated circuit that compares the input and output signals to compute impedances, changes in magnitude, and / or changes in phase.

[0281] Compressed sensing-based neural network. The most notable area for improvement with the CS-based NN is the mesh resolution. A 24 * 24 mesh was chosen primarily to speed up development, and there were also size considerations for NN deployment. As one would expect, increasing the mesh resolution would exponentially increase the number of trainable parameters. As stated before, there is no reliance on expected output data, therefore the same datasets could theoretically be used to train a higher resolution model. The only modifications needed would be to update the Jacobian and ensure the dense layers have the appropriate number of nodes to match the output. Now that the workflow has been established, improving image resolution should be straightforward. Alternatively, a new hybrid neural network could be developed that combines both compressed sensing and traditional deep learning techniques. The overall architecture would resemble that of an encoder-decoder network. In other words, the CS- based NN serves as the encoder that encapsulates information about the sensing domainthrough the Jacobian. Convolution and upscaling layers could then be used to “decode” the encoder’s output into the final high-quality reconstruction.

[0282] Edge intelligence. Other forms of edge intelligence can be deployed. Simpler NNs could be used to classify whether damage is present in the sensing domain. Another option could be to classify the severity of damage. These are all alternatives that could still be beneficial for continuous structural health monitoring applications.

[0283] EIT sensing materials . EIT can theoretically be performed on all conductive materials. This opens the possibility of applying EIT to structures 3D printed with conductive filaments (e.g., PLA and TPU). Preliminary tests showed that 3D printed sheets of conductive TPU behave similarly to the UHMWPE used in the present disclosure. Preliminary tests show that it was possible to spatially locate damage in conductive TPU. The idea of 3D printed EIT sensors is fascinating and should be explored in future research.Second Example of Electrical Impedance Tomography Data Acquisition System with Deep Learning Edge Computing FunctionalityHardware Specifications

[0284] A second example of the electrical impedance tomography (EIT) data acquisition (DAQ) being developed occupies an even smaller spatial footprint (59 x 64 x 25 mm3) by utilizing a four-layered printed circuit board (PCB) (Figure 52A) and can be wirelessly interfaced with a smartphone. The new DAQ system (Figure 52B) supports both alternating current (AC) and direct current (DC) measurement modalities which will support a wider range of materials with various electrical properties. Depending on the material, the onboard voltage- to-current converter is capable of outputting currents between 0.1 mA and 100 mA. The voltage differentials are measured by an instrumental amplifier which then feeds into a precision rectifier before reaching the analog-to-digital converter (ADC). The AC signal generator supports frequencies between 0 - 100 kHz.

[0285] Multiplexer (MUX) Array. The new DAQ system (Figure 52B) uses four ADG706 MUXs as opposed to the three ADG732 MUXs in the previous example. The additional MUX allows for adjacent voltage measurements whereas previously, voltages were measured relative to ground.

[0286] Current Source. An OPA189 zero-drift op amp is implemented as a voltage-to-current converter that takes in a reference voltage and outputs a corresponding constant current. Thereference voltages can either be AC or DC. For the DC reference voltage, PWM out of the nRF52840 is passed through a low pass filter to convert it into a constant voltage. For the AC reference voltage, the signal generator on the AD5933 is passed through a high-pass filter to remove any DC offsets before entering the voltage-to-current converter. There is a 3-pin junction that corresponds to DC reference, AC reference, and reference in. A shunt connector allows the user to switch between AC and DC current sources. Both AC and DC references are programmable to modulate frequency, PWM duty cycle, etc.

[0287] Instrumental Amplifier and Precision Rectifier . An INA188 instrumental amplifier was chosen to amplify the voltage differentials from the measurement MUXs. The amplified signal passes to a precision rectifier to rectify AC signals into DC before going to the analog-to-digital converter. The precision rectifier is comprised of an OPA2189 with a AD8628 op amp as a buffer.Edge Computing

[0288] To address the hardware limitations encountered in the previous generation of the DAQ system (z.e., lack of memory and computational power), a deep learning (DL)-based algorithm is being developed for EIT reconstructions.

[0289] Motivation. There are several factors that make deep learning favorable for this application. Deep neural networks have proven effective in picking up nonlinearities for ill- posed problems which is extremely relevant to EIT reconstructions. Deep learning reconstructions are also significantly faster than traditional iterative approaches since can utilize as little as just one pass through the neural network (NN), as compared to potentially tens of thousands of iterations. Lastly, there has been a recent surge of support for deploying machine learning algorithms onto edge devices (z.e., Edge Impulse).

[0290] Traditional methods for applying DL tend to brute forcing the model performance by adding more data and complexity. As mentioned previously, there is limited onboard memory, so the reconstruction algorithm must be optimized for size and efficiency. An approach was developed that leverages compressed sensing (CS) to strategically train the neural network.

[0291] Compressed Sensing-Based Neural Network. A common compressed sensing algorithm used is the iterative shrinkage / thresholding (1ST) algorithm, which attempts to solve the following objective function:where 6a is the change in conductivity, J is the Jacobian for the sensing domain, 6V is the change in boundary voltage distribution between the homogeneous and inhomogeneous state, is the regularization parameter, and ||<5cr||i, is the Li-norm of 6a. This objective function attempts to find a set of 6a that matches closely with the given 6V when transformed by Jacobian, J. The Li-norm is added to promote sparsity which greatly aids the ill-posed nature of this inverse problem. controls how much influence the Li-norm has which can help with noisy reconstructions. This objective function could be leveraged by deep learning to train a neural network.

[0292] Deep learning includes three things: input data, expected output data, and a loss function (z.e., a metric to evaluate how well the neural network performs). During training, the NN output is compared to the expected output and evaluated using a loss function. A common loss function used for deep learning regression models is mean squared error (MSE) which can be calculated by:where ytis expected output value from the training dataset and ytis the NN output value. During training, the calculated loss is fed into an optimizer that adjusts the weights in each layer of the NN to minimize loss.

[0293] Because the goal of the optimizer is to minimize a computed numerical value, Equation (1) can be modified to serve as a loss function for NN training. In the loss function:where the NN output, do, is transformed with J and compared with the NN input, 6V. Rather than having the NN pickup information from patterns in the training dataset, information is picked up using the custom loss function instead.

[0294] Neural Network Architecture . The architecture of the NN is a time-unfolded version of the traditional 1ST algorithm which essentially means that each section of the NN corresponds to a specific iteration in time. In each section of the NN, custom activation functions are used that handle the “thresholding” part of 1ST. The NN architecture is visually represented in Figure 53.

[0295] The final DL algorithm will be deployed onto the DAQ system via Edge Impulse to perform EIT reconstructions. Each reconstruction is anticipated to take -400 ms, which is a significant improvement to the current deployed two step iterative shrinkage / thresholding (TwIST) that takes several minutes.Applications

[0296] The new DAQ system itself is capable of producing reconstructions in real time. In the field of EIT DAQ systems, this feature is unprecedented. All known portable EIT DAQ systems rely on streaming data to an external computer for analysis. All machine learning implementations for EIT are also performed on an external computer. With a dedicated smartphone app, the EIT DAQ can be operated wirelessly, and reconstructions can be directly plotted on the app. Modifications to the developed NN can allow the DAQ system to alert the user in the presence of an anomaly.Autonomous Damage Detection and Localization for Carbon Fiber-Reinforced Polymer Composites via a Novel Electrical Impedance Tomography System with Edge Intelligence

[0297] Electrical Impedance Tomography . The EIT technique includes forward and inverse problems. The forward problem solves for the boundary voltage of a conductive medium based on an assumed internal conductivity distribution. To do so, the simplified 2D Laplace equation7 ■ (oVv) = 0 in fl is used to ensure that the current flowing into the domain equals the current flowing out. This is then combined with a finite element model represented by a set of linear equations to obtainwhere 4(cr) is an invertible square matrix, I is the injected current across the domain, and b is a coefficient vector of elemental nodal potentials which includes the boundary electrode voltages to be solved for in the forward problem. On the other hand, the inverse problem attempts to do the opposite: solve for the internal conductivity distribution based on an assumed boundary voltage distribution. Solving the inverse problem often involves minimizing the difference between the estimated boundary voltages and the assumed boundary voltages. In other words, the internal conductivity is iteratively modified such that its corresponding boundary voltages match closely with the target boundary voltages. This relationship can be represented aswhere a* is the estimated internal conductivity, is the estimated boundary voltages corresponding to a* (i.e., solved via the forward problem), and gyasuredisthe target boundary voltage distribution. By solving the inverse problem, materials’ internal conductivity distribution can be reconstructed, where conductivity changes can correlate to anomalies in the materials (e.g., damage in the CFRPs). Because the inverse problem is severely ill-posed, most reconstruction algorithms iteratively regularize the outputs to obtain a stable converging solution.

[0298] Deep Learning and Edge Intelligence. Given the numerical nature of EIT, many research endeavors have focused on incorporating machine learning and artificial intelligence. Deep learning (DL), specifically, has received a lot of attention due to its ability to handle ill- posed problems and extract nonlinear patterns from data. Current DL-based EIT reconstruction can be categorized into three different types: direct, joint, and hybrid reconstruction. Direct reconstruction converts voltage measurements into the corresponding conductivity distribution. See e.g, Li et al., “Comparison between a novel compressed sensing-based neural network and traditional neural network approaches for electrical impedance tomography reconstruction,” Proc. SPIE 12951, Health Monitoring of Structural and Biological Systems XVIII, 1295111, 2024; which is hereby incorporated by reference in its entirety herein. Joint reconstruction method uses DL neural networks (NNs) in conjunction with other traditional techniques to output a high-quality reconstruction. One of the notable reported examples is the Deep D-Bar technique, where low-resolution outputs from traditional D-Bar are passed through a deep NN to refine the reconstruction and even outline anomalies e.g., organ boundaries in medical imaging). Lastly, hybrid reconstruction combines multiple DL NNs to perform the full reconstruction: one for the initial direct conductivity mapping and another for further image refinement. While DL could significantly improve the EIT reconstruction, currently reported models tend to be not versatile enough for unpredictable experimental data. In addition, although incorporating edge intelligence in the sensing systems is an essential step towards achieving autonomous assessment of structural composite conditions, current DL models are mostly large in size and not compatible with edge deployment.

[0299] Regarding edge intelligence for EIT analysis, DL can be a far more favorable approach compared to traditional algorithms. For one, traditional EIT reconstruction algorithms are iterative, requiring tens of thousands of iterations before the solution converges. Suchoperations are very challenging for edge devices with limited computing and memory capacities. Also, inferences via DL NNs can take significantly shorter time. In fact, as a first ever reported attempt to implement edge intelligence for EIT, each traditional reconstruction took about seven minutes for a microcontroller to complete. Therefore, this work aims to develop an edge deployable DL model to perform EIT analysis in a far more efficient (e.g., in milliseconds) and autonomous manner.Method Details

[0300] Design of a Portable EIT DAQ Hardware System. An example design of a portable EIT DAQ hardware system is described herein.

[0301] Microcontroller . The microcontroller chosen for the present disclosure was the Arduino Nano 33 BLE. This microcontroller, powered by an nRF52840, offers one of the largest onboard memory capacities currently available. While some microcontrollers may have more available memory, they lack one or more features which were deemed important for the application, such as built-in Bluetooth Low Energy (BLE) capability, sufficient general- purpose input / output (GPIO) pins, and a development board with a small spatial footprint.

[0302] Multiplexer array. To support four-pole EIT measurements, four multiplexers (MUXs) were needed: one to establish a path for current to flow in, one for current to flow out, and two to measure adjacent voltage differences across electrode pairs. Several GPIO pins were reserved: one input pin for the analog-to-digital converter (ADC) to measure the voltage differential, and one output pin to control the flow of current when performing EIT measurements. The final DAQ system developed in the present disclosure could support up to 16 electrodes for EIT. The ADG706 MUX was chosen for its low power consumption, low operation resistance, and fast switching times.

[0303] Constant current source. One of the most crucial parts of an EIT DAQ system is the constant current source (CCS). Constant current was used as opposed to constant voltage because it could minimize the influence of electrode impedance. The implementation of a CCS consisted of an operational amplifier (op-amp) configured as a voltage-to-current converter, where the current was controlled by the bias resistor and an input voltage. The input voltage was provided by a two-stage low-passed pulse-width-modulated (PWM) signal from the Arduino Nano 33 BLE.

[0304] Figure 54 illustrates the interactions of the major components in the DAQ system during operation.

[0305] Figures 55A-55B shows images of the assembled DAQ hardware.

[0306] Development of DL-Based Edge Intelligence Functionality . The design and training of a lightweight DL model is described herein.

[0307] The present disclosure also aims to develop a novel DL model optimized for edge deployment so that the EIT hardware system can autonomously perform data analysis and provide human inspectors with informative damage indicators to facilitate the maintenance of structures. To be specific, the present disclosure designed a model that could perform both classification and regression to identify and locate an anomaly in the test domain. This was represented by two sets of outputs: the first provided a classification confidence that indicated whether an anomaly was present; the second provided the location of the identified anomaly in the form of x- and y-coordinates. Note that for practical applications, the positional output should be ignored if the model does not detect an anomaly (e.g., the classification confidence is less than 50%).

[0308] Figure 56 depicts the architecture of the lightweight DL model. The model consisted of two-dimensional (2D)-convolutional and fully connected layers. The inputs for the model were boundary voltage measurements. Each set of measurements was formatted into a 16x 13 image, with each row representing a set of 13 measurements corresponding to a single injection-ground electrode pair. The first three layers of the model were convolutional with max pooling layers, which reduced the image resolution by half each time. This architecture was designed to reduce the total number of parameters such that the model could be small enough in size to be deployed onto the DAQ hardware. The output of the third max pooling layer was flattened and fed into two fully connected layers successively. The second fully connected layer then branched out into two 1x2 outputs, corresponding to classification confidence and anomaly position coordinates, respectively.

[0309] The training dataset was created using the Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software (EIDORS) for a 16-electrode configuration and consisted of 4000 anomaly cases and 4000 non-anomaly cases. For each anomaly case, one circular anomaly with varying size, conductivity, and location was introduced to the test domain. The ranges of these parameters are listed in Table 2. The EIT forward problem was solved for each training case to generate its corresponding simulatedboundary voltage values. These voltages were subtracted by the theoretical baseline values (z.e., when no anomaly existed in the test domain and no noise existed in measurements) and normalized by the maximum value in the baseline set to yield the model input. The normalization process could render the DL model independent of specific electrical properties of the test materials. Eight thousand datasets were generated, 80% of which were used for training and the other 20% for validation. Gaussian noise was also added to the voltage measurements such that the signal-to-noise ratio (SNR) was 65 dB. Note that the DAQ hardware developed in the present disclosure was expected to have a much lower noise level of ~80 dB. The model was trained on noisier data so that it could be more robust for unpredictable experimental measurements.TABLE 2. TRAINING DATASET FOR ANOMALY CASES.Anomaly Parameters Minimum MaximumSize (% of domain area) 1 20Conductivity change 0 (exclusive) 0.5Minimum distance to edge (% of domain length) 25 50

[0310] The model was trained with a learning rate of le-3 using the Adams optimizer. Training was performed over 100 epochs, so that both the training and validation losses could reach a steady level. For the classification output, the binary cross-entropy loss, also known as log loss, was used. This layer used the Softmax activation to ensure that the classification probabilities summed to 1. For the positional output, the mean-squared error (MSE) loss was used. This output layer had no activation. In addition, L2 regularization and dropout were employed to prevent overfitting. The regularization parameter was adjusted to minimize both overfitting and loss, and a final value of 0.05 was determined.

[0311] It was expected that the trained DL model would behave differently depending on the size, conductivity, and location of an anomaly, in addition to the level of noise in the measurements. Thus, to rigorously evaluate the performance of the developed DL model and determine its inference limitations, a series of computational studies was first performed. Here, all the test cases were generated using EIDORS, where the EIT forward problem was solved to generate boundary voltage measurements.

[0312] First, to investigate how accurately the model could classify non-anomaly cases against different noise levels, Gaussian noise was introduced to the voltage measurements where no anomaly existed, such that the SNR varied from 25-85 dB. The classification confidence ofthe DL model was then evaluated and averaged. Theoretically, above a certain SNR threshold, the DL model should infer that no anomaly existed (i.e., ground truth) with high confidence.

[0313] Furthermore, to investigate how well the DL model could identify and locate anomalies with varying features (i.e., size, conductivity, and location), test cases with one anomaly were generated following the variable ranges summarized in Table 3. Figure 57 illustrates the configuration of an example test case. 65 dB of Gaussian noise was also added to the simulated voltage values. Performance heatmaps were generated to characterize the model performance (i.e., classification confidence and predicted position error) under different combinations of anomaly features. Each cell within the heatmaps represents the average model performance over ten random anomaly cases with features corresponding to that cell.TABLE 3. SIMULATED TEST DATASET FOR ANOMALY CASES.Anomaly Parameters Ranges IntervalsSize (% of domain area) (0, 5] 0.2Conductivity change (0, 0.9] 0.1Minimum distance to edge (% of domain length)

[0550] 5

[0314] Edge deployment of the DL model. To further reduce the size of the trained model for edge deployment, the weights were converted and scaled from floats to 8-bit integers. Similarly, the inputs, outputs, and intermediate activations were converted and scaled from floats to 16-bit integers. This process was carried out using TensorFlow Lite Micro. The resulting model file was compiled with the main program and deployed onto the Nano 33 BLE board. Before deployment, both quantized and unquantized versions of the model were tested with 1000 anomaly cases from the training set.

[0315] Damage Detection and Localization Experiments. Damage detection and location experiments were conducted and are described thusly.

[0316] Preparation of CFRP test samples. To investigate how versatile the developed EIT DAQ hardware and DL model were for different carbon fiber layouts i.e., different electrical properties) and 3D geometries of CFRP composites, the present disclosure implemented the EIT system on arbitrarily selected commercial CFRP composites, including planar and highly curved geometries. To be specific, the planar test samples were fabricated from commercial CFRP panels (FAKILO, 200x300* 1 mm3) with a twill carbon fiber weave composed of fibers oriented at 90 degrees to each other. Test samples were first cut into 100* 100* 1 mm3 squared pieces. As seen in Figure 58A, 16 boundary electrodes, made from 3 mm-wide copper foiltapes, were evenly attached to the surface of each sample. Conductive silver paint (Ted Pella, Inc.) was applied over the copper tapes to minimize contact resistance of electrodes. Note that no further surface processing was needed to perform the spatial damage detection experiments.

[0317] In addition, curved CFRP test samples, representing complex 3D geometries that are typically challenging for common NDE approaches, were also prepared and tested. Here, the samples were fabricated using an arbitrary CFRP pipe (Streamline Aerospace, Inc.) which had a 5-layer carbon fiber layout. This layout consisted of the first layer being bidirectional with a ±45-degree weave, followed by 3 layers of unidirectional fibers (0 degree), and the last layer being bidirectional with the same ±45-degree weave. Figure 58B and Figure 58C show the schematics of sample configuration. The samples were cut such that the length and the curved edge were both 100 mm (z.e., same dimensions as the planar samples except for the geometry). The electrodes were established in the same manner using copper tapes and silver paint without any further surface modifications. It indicated that the EIT system developed in the present disclosure was remarkably compatible with various commercial CFRPs.

[0318] EIT measurements and damage reconstruction. The present disclosure generated a series of damage cases on both planar and curved CFRP specimens to experimentally characterize the robustness of the developed EIT hardware and deployed DL model. Here, the damage was introduced in a sequential manner to emulate damage development or the occurrence of new damage. For instance, a small-sized hole might be first drilled on a sample, which might then be drilled into a larger one (z.e., damage growth), or a new hole might be drilled at a different location (z.e., new damage). For each damage case, baseline EIT measurements were collected in advance, where the injection current was also calibrated to accommodate different electrical properties of the CFRPs. Upon introducing the damage, new measurements were performed and recorded. The baseline and the new measurements were then input into the deployed DL model to infer the existence of new damage and to predict the spatial coordinates of the damage onboard, which were compared with the actual location. In addition, based on the damage size and location, the inference outputs of the deployed DL model were compared with the computational values summarized in the heatmaps. This would enable the transferability and robustness of the DL model when using experimental data.

[0319] Furthermore, similar to other existing EIT research, the present disclosure also utilized computer-based iterative algorithms to solve the EIT inverse problem and reconstruct conductivity maps. Here, a two-step iterative shrinkage / thresholding (TwIST) algorithm wasadopted for its relatively high reconstruction accuracy and resolution. More details on the TwIST algorithm and its EIT applications can be found in Li et al., “Development of a Portable and Low-Cost Data Acquisition System With Edge Intelligence for Electrical Impedance Tomography-Based Spatial Damage Detection,” IEEE Transactions on Instrumentation and Measurement, vol. 73, pp. 1-11, 2024; which is hereby incorporated by reference in its entirety herein. The goal was to not only validate the performance of the EIT hardware by visualizing the reconstructed damage distribution but also compare with the outputs from the deployed DL model, which was especially valuable for identifying cases where the model prediction lacked confidence or had high position errors.Results and Discussion

[0320] Performance of the DAQ Hardware. For EIT measurements, it is extremely crucial that the injected current remains constant for a wide range of loads across the CCS. To evaluate its performance, a known resistance was placed across the CCS and the voltage drop across the load was measured using a Keysight 34465A Digital Multimeter. The resistance and voltage drop values were used to determine the current across the load via Ohm’s Law. Resistors ranging from 0.68-22.7 kOhms were used as the load, and the CCS was configured to be 0.1, 0.2, and 1.0 mA. whose corresponding voltage measurement results are shown in Figure 37.

[0321] One can observe a highly linear relationship between the load and the load voltage, which was consistent with Ohm’s Law. It suggested that the CCS was able to maintain a constant current as the load varied. All these trendlines did not exceed 3 V because the CCS was powered by the regulated 3.3V from the microcontroller. It was verified that the same current could be maintained as different pairs of adjacent electrodes were connected to the CCS during the EIT measurement process.

[0322] Then, the measurement quality of the entire DAQ hardware system was assessed by performing the EIT measurement scheme on a 100x 100x 1 mm3squared CFRP composite sample. The measured voltage values were normalized and compared with theoretical simulations from EIDORS, where the EIT forward problem was solved for a homogenous domain with uniform conductivity. Figure 44 shows the comparison between the experimental measurements and theoretical values, which demonstrated a remarkably similar trend. Minor discrepancies could likely be attributed to imperfections in electrode spacing on the test sample. Thus, it was reasonable to assume that the commercial CFRP test specimen had a uniformconductivity distribution owing to the weaved carbon fibers. Overall, this comparison test demonstrated that the designed DAQ hardware system was not only capable of outputting accurate measurements, but also compatible with the CFRP composites to perform EIT-based damage detection.

[0323] Performance of the Lightweight DL Model. The performance of the lightweight DL model is described as follows.

[0324] Model training performance. Two metrics were used to assess the accuracy of the DL model during training, one for each output type. The classification output was evaluated with the binary accuracy metric calculated using the following equations in Keras.where n represents the total number of data samples, / ? / : is the model classification confidence for a sample k, and & is the ground truth value for the sample k (i.e., 0 or 1 representing the absence or existence of an anomaly, respectively).

[0325] On the hand, the positional output (pkx, pky) was evaluated using a custom metric which calculated the Euclidean distance between the predicted and true positions (tkx, tky) of the anomaly in the sample k, as shown in the following equation.The total loss was the sum of the classification and regression losses. Figure 59A shows that the classification accuracy increased significantly within the first few epochs, but dropped slightly in later epochs, whereas the position error continued to decrease (Figure 59B). The total loss, shown in Figure 59C, dropped immediately within the first few epochs and decreased at a more gradual pace before stabilizing close to the 100th epoch. The different behaviors of classification and regression losses during training could be due to the model being incentivized to minimize the total loss rather than the individual losses in conjunction. This behavior could be minimized through further branching of the DL model architecture but at the expense of increasing model size, which was undesirable for edge deployment. It shouldalso be noted that all validation metrics performed better than those for training, which signified that regularization and dropout effectively minimized overfitting during training.

[0326] Computational evaluation of the trained model. The model’ s classification performance was first tested with different levels of noise in the voltage measurements when no anomaly existed. Figure 60 demonstrates that the model’s negative classification confidence (i.e., how confident it was that an anomaly was not present in the test domain) increased with the SNR of the voltage measurements. This trend was expected, because higher SNRs would reduce the risk for the model to misidentify noise as an anomaly in the test domain. Even at ~55 dB SNR, the model could already provide accurate classification with 90% confidence, which indicated the trained model could be robust against noisy experimental data.

[0327] In addition, the present disclosure also comprehensively evaluated the DL model classification and position prediction accuracy with thousands of simulated anomaly test cases. Figures 61A-1C show the average classification confidence distributions across different combinations of anomaly size and location. Because the ground truth was that an anomaly existed in the domain, a higher prediction confidence (i.e., closer to 1) would reflect better model performance. Contour lines were added to these heatmaps to highlight regions of high and low classification accuracy, which were 0.9 and 0.5, respectively. It can be observed that model classification accuracy increased with anomaly size and decreased with distance to edge, regardless of the conductivity of the anomaly. This trend indicated the model could more accurately detect damage cases that are large and closer to boundaries, which agreed with theoretical intuition.

[0328] Similarly, Figures 62A-62C show the distributions of average position error of predicted anomaly across different combinations of anomaly size and location. Here, the hatched regions corresponded to the test cases where the model failed to positively identify the anomaly (classification confidence less than 0.5), and positional output was therefore irrelevant. Contour lines were also added to the heatmaps to demonstrate regions with small and large position errors, which were defined as 5%, 20% of the test domain length as an example, respectively. These contour lines could be readily defined by structural inspectors in practice to more efficiently interpret model outputs. Figures 62A-62C indicate that position error decreased with anomaly size, but anomaly location had more complex effects on position error.

[0329] Besides, Figures 61A-61C and Figures 62A-62C show that when the change in the conductivity of anomaly became more significant, the regions of high classification accuracy and low position error increased on the heatmaps. It suggested that the model tended to more accurately identify and locate the damage that would induce larger change in conductivity of the test materials. Also, it is worth noting that the model performed significantly better as the change in anomaly conductivity increased from the range of 0-0.1 to 0.4-0.5, whereas slight improvement occurred from 0.4-0.5 to 0.8-0.9. This indicated that the trained model could capture damage of a wide range of severity with a relatively high accuracy.

[0330] Furthermore, prior to deploying the model onto the microcontroller, the effects of quantization on model performance were investigated. Table 4 summarizes the key performance of unquantized and quantized models. Evidently, the quantization significantly reduced model inference time and model size by -63% and -85%, respectively, without compromising the model inference accuracy.TABLE 4. MODEL PERFORMANCE COMPARISON.Performance Metrics Unquantized Model Quantized ModelModel size (kB) 339.7 52.5Average classification accuracy 0.913 0.912Average position error (% of domain length) 7.572 7.573Average inference time (ms) 470 176

[0331] EIT-Based Damage Detection and Localization. To evaluate the performance of the DAQ hardware, experimental measurements on CRFP samples were first used for TwIST algorithm-based damage reconstructions. Note that because the goal was to capture the occurrence of any new damage, each damage was sequentially introduced and measurements from the previous case were used as the baseline for reconstruction. Figures 63A-63E exhibits each damage case on a planar sample, and Figures 64A-64E shows the correspondingly reconstructed conductivity maps, where the regions with decreased conductivity indicated the detected anomalies. TwIST algorithm was able to identify and locate all the new damage (including the growth of existing damage), except for Test Case #1. Minor damage in the central region was expected to be challenging for the EIT technique to capture.

[0332] Similar damage reconstruction tests were conducted on a highly curved geometry. Figures 65A-65C show a curved CFRP sample with sequentially introduced damage, and Figures 65D-65E show their reconstructed conductivity maps, respectively. Clearly, all thedamage cases were mapped relatively accurately. Overall, it suggested that the EIT DAQ hardware could provide high-quality measurements for different material conductivities and geometries.

[0333] In addition, those experimental measurements were also analyzed using the deployed DL model. The model performance was compared with the computational evaluation, particularly with change in anomaly conductivity at 0.8-0.9 (Figure 61C and Figure 62C) to approximately represent the damage in experiments. Figure 66A summarizes the classification confidence for each test case of the planar sample based on experimental or simulated data. The DL model exhibited higher inference confidence with the experimental data than simulations. This was most likely because the DAQ hardware could provide high-quality measurements that had a lower noise level than the 65 dB noise introduced to the computational test cases. Also, as damage grew larger, the model’s confidence increased, as expected. The classification confidence correlated well with the visibility of the anomalies reconstructed by the TwIST algorithm. It is worth noting that although the TwIST could not capture the small central damage in Test Case 1, the DL model was able to identify the damage with almost 60% confidence.

[0334] Figure 66B shows the position errors tested with experimental and simulated data. The experimental performance of the DL model indicated that the position error generally reduced as the anomaly increased in size. There was no apparent difference in model performance when the anomalies located in the center or at the corner of the test domain. Note that for Test Case 1, due to the low classification confidence in simulation (less than 20%), simulated position error was not considered.

[0335] Similarly, Figure 67A and Figure 67B summarize the classification confidences and position errors of the DL model based on experimental and simulated data of the curved sample, respectively. Again, the DL model showed higher inference confidence and smaller position error for experimental data, which was probably due to the higher SNR of the experimental measurements. Note that for Test Cases 2 and 3, because the damage is small, the model had low confidence (below 50%) when analyzing the simulation data, hence simulated position errors were not considered. Moreover, the average time for all inferences performed by the deployed model on the hardware was 176 ms.Conclusions

[0336] The goal of the present disclosure was to develop a novel EIT DAQ system with edge intelligence functionality to potentially achieve autonomous condition assessment for CFRP composites. In particular, an electronic hardware system was first strategically designed to maximize functionality and minimize spatial footprint. Benchmark tests have verified that the designed DAQ system could provide high-quality EIT measurements and was compatible with the electrical property of CFRPs. To achieve the edge intelligence functionality, a lightweight DL model was developed to identify and locate the presence of an anomaly within the sensing domain. The model utilized both convolutional and dense layers to output classification confidence and coordinates of the predicted anomaly. The trained DL model was then reduced in size by -85% via quantization and was deployed onto the DAQ hardware. The deployed DL model could run simultaneously with EIT measurements.

[0337] Model performance was first computationally evaluated in terms of classification confidence and position error for a wide range of simulated anomaly data of varying size, conductivity, and position across the test domain. It was found that the classification confidence increased with anomaly size and decreased with distance to edge. The position error decreased with anomaly size, but anomaly location had more complex effects. Model inference accuracy improved as the change in anomaly conductivity became more significant. Furthermore, the DAQ system with the deployed DL model was implemented to locate damage on CFRPs of different electrical properties and 3D geometries. It was verified that the DAQ hardware could provide high-quality EIT measurements for identifying the damage with either traditional EIT algorithms or the DL NN. Regardless of the complex experimental conditions (e.g., noisy signals, different electrical properties, and complex geometry), the deployed DL model could not only perform onboard data analysis very efficiently (176 ms per inference), but also capture the damage with high accuracy.

[0338] Overall, the present disclosure successfully developed a highly compact EIT DAQ system coupled with an edge-deployed DL NN that was capable of autonomously collecting and analyzing data and informing human inspectors about occurrence and location of potential damage on CFRPs. It represents a significant step towards automating the monitoring and inspection of the integrity of CFRP structural components, which is especially valuable in the operating environment where computational resources are limited. Future work can potentiallyfocus on improving the DL model to output more informative anomaly features, such as damage size and severity, to better alert users of the CFRP conditions.

[0339] From the foregoing, it can be seen that the present disclosure accomplishes at least all of the stated objectives.GLOSSARY

[0340] Unless defined otherwise, all technical and scientific terms used above have the same meaning as commonly understood by one of ordinary skill in the art to which embodiments of the present disclosure pertain.

[0341] The terms “a,” “an,” and “the” include both singular and plural referents.

[0342] The term “or” is synonymous with “and / or” and means any one member or combination of members of a particular list.

[0343] As used herein, the term “exemplary” refers to an example, an instance, or an illustration, and does not indicate a most preferred embodiment unless otherwise stated.

[0344] The term “about” as used herein refers to slight variations in numerical quantities with respect to any quantifiable variable. Inadvertent error can occur, for example, through use of typical measuring techniques or equipment or from differences in the manufacture, source, or purity of components.

[0345] The term “substantially” refers to a great or significant extent. “Substantially” can thus refer to a plurality, majority, and / or a supermajority of said quantifiable variables, given proper context. The term “generally” encompasses both “about” and “substantially.”

[0346] The term “configured” describes structure capable of performing a task or adopting a particular configuration. The term “configured” can be used interchangeably with other similar phrases, such as constructed, arranged, adapted, manufactured, and the like.

[0347] Terms characterizing sequential order, a position, and / or an orientation are not limiting and are only referenced according to the views presented.

[0348] The “invention” is not intended to refer to any single embodiment of the particular invention but encompass all possible embodiments as described in the specification and the claims. The “scope” of the present disclosure is defined by the appended claims, along with the full scope of equivalents to which such claims are entitled. The scope of the disclosure is further qualified as including any possible modification to any of the aspects and / or embodiments disclosed herein which would result in other embodiments, combinations, subcombinations, or the like that would be obvious to those skilled in the art.

Claims

CLAIMSWhat is claimed is:

1. A method for reconstructing the conductivity of materials directly through neural networks (NNs), the method comprising: using deep learning (DL) to train a compressed sensing (CS)-based NN architecture with a loss function that transforms the NN output with a Jacobian and compares the transformed NN output with the NN input; and capturing electrical properties and characteristics of a sensing domain.

2. The method of claim 1, further comprising leveraging an objective function in the compressed sensing technique to formulate the custom loss function.

3. The method of claim 1, wherein information regarding the sensing domain is extracted from a Jacobian in the custom loss function rather than data.

4. The method of claim 1, wherein the training uses only simulated training data.

5. The method of claim 1, further comprising injecting small electrical currents across an area of interest to characterize a conductivity distribution.

6. The method of claim 1, wherein the training is free from minimizing the mean squared error (MSE) between a predicted output and a true output.

7. The method of claim 1, further comprising evaluating a reconstruction resolution of said training.

8. The method of claim 1, further comprising evaluating an accuracy metric of said training.

9. The method of claim 1, further comprising using the NN architecture to identify a propagating crack in concrete or to identify impact damage and delamination in a carbon fiber-reinforced composite.

10. The method of claim 1, further comprising using the NN architecture to monitor lung ventilation or brain activity.

11. The method of claim 1, further comprising using the NN architecture to diagnose a tumor.

12. The method of claim 1, further comprising incorporating an electrical impedance tomography (EIT) technique into a wearable or an implantable technology.

13. The method of claim 1, further comprising identifying a position of a body.

14. The method of claim 1, further comprising performing analysis on low-powered edge devices.

15. A standalone electrical impedance tomography (EIT) data acquisition (DAQ) system capable of performing analysis comprising: a microcontroller with memory to store a neural network; a multiplexer that supports adjacent voltage measurements; and an instrumentation amplifier to amplify voltage differences across the electrodes.

16. The standalone EIT DAQ system of claim 15, wherein the microcontroller comprises direct current (DC) circuitry.

17. The standalone EIT DAQ system of claim 16, wherein the DC circuitry comprises a multistage instrumentation amplifier.

18. The standalone EIT DAQ system of claim 16, further comprising a digital potentiometer to control a gain with software.

19. The standalone EIT DAQ system of claim 16, wherein an external resistor is placed between pins on a chip to control the gain.

20. The standalone EIT DAQ system of claim 16, wherein the DC circuitry is free from a precision rectifier.

21. The standalone EIT DAQ system of claim 16, further comprising a precision rectifier with an op-amp that operates between ±5V.

21. The standalone EIT DAQ system of claim 21, further comprising an additional opamp configured as a voltage follower to serve as a buffer and to protect an onboard ADC by limiting the output voltages to the precision rectifier.

22. The standalone EIT DAQ system of claim 15, wherein the microcontroller comprises alternating current (AC) circuitry.

23. The standalone EIT DAQ system of claim 22, wherein the AC circuitry comprises an impedance analyzer.

24. The standalone EIT DAQ system of claim 22, wherein the AC circuitry comprises a signal demodulator.

25. The standalone EIT DAQ system of claim 22, further comprising an alternating current (AC) injection mode wherein there are a range of frequencies where bioimpedance is lowest due to its inherent capacitive characteristics.

26. The standalone EIT DAQ system of claim 15, wherein a voltage-to current converter (VCC) allows for both AC and DC current injection.

27. The standalone EIT DAQ system of claim 15, wherein the multiplexer is a 4 MUX architecture.

28. The standalone EIT DAQ system of claim 27, wherein the multiplexer comprises only sixteen electrodes.

29. The standalone EIT DAQ system of claim 15, further comprising positive and negative power rails.

30. The standalone EIT DAQ system of claim 15, further comprising a modified TwIST algorithm deployed onto the system to perform on-board image reconstructions using a course element mesh.

31. A modified TwIST algorithm comprising: an objective function comprising:wherein: 6a is a change in conductivity, J is a Jacobian for the sensing domain, 6V is a change in boundary voltage distribution between a homogeneous and inhomogeneous state, is a regularization parameter, and ||6CT|| is the Li-norm of 6a, and the NN output, 6a, is transformed with J and compared with an NN input, <57; and an edge computing functionality.

32. The modified TwIST algorithm of claim 31, wherein a hyperparameter controls the magnitude of the Jacobian during training.

33. A neural network (NN) architecture comprising: a surrogate model trained to mimic a compressed sensing algorithm that performs the electrical impedance tomography (EIT) conductivity reconstruction; a mesh resolution of at least 24 x 24.

34. The NN architecture of claim 33, further comprising a soft thresholding function used in an iterative shrinkage / thresholding (1ST) that sets values to zero if they fall within a certain threshold.

35. A compressed sensing (CS)-based neural network (NN) architecture comprising:a mapping layer that allows voltage data to pass therethrough, wherein said voltage data is allowed to then branch off to compute the residual and gradient before merging back with the mapping layer; an input data mapped using the transformation matrix, wherein the input data iteratively passes through shrinkage and thresholding functions until an ending criteria is met; and36. The CS-NN architecture of claim 35, wherein the ending criteria is a max number of iterations.

37. The CS-NN architecture of claim 35, wherein the ending criteria is a converging loss.

38. The CS-NN architecture of claim 35, wherein the NN architecture unfolds the iterative portion and represents each individual iteration as a separate series of layers in the neural network (NN).

39. The CS-NN architecture of claim 35, wherein the mapping layer is a dense layer serves as a learned Jacobian.

40. The CS-NN architecture of claim 35, further comprising an objective function comprising:wherein: 6a is a change in conductivity, J is a Jacobian for the sensing domain, 6V is a change in boundary voltage distribution between a homogeneous and inhomogeneous state, is a regularization parameter, and ||6CT|| is an Li-norm of 6a, and an NN output, 6a, is transformed with J and compared with an NN input, 6V.

41. The CS-NN architecture of claim 35, further comprising a soft thresholding function used in an iterative shrinkage / thresholding (1ST) that sets values to zero if they fall within a certain threshold.

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