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DOE OSTI2023

Spread Spectrum Time-Domain Reflectometry and Frequency Domain Reflectometry to Detect Shielded and Unshielded Cable Moisture Exposure

This work evaluates the feasibility to extend spread spectrum time-domain reflectometry (SSTDR) and frequency domain reflectometry (FDR) electrical cable testing to characterize whether an electrical cable is submerged in water or not and where it may be submerged. Using PNNL’s ARENA cable and motor test bed, shielded and non-shielded electrical cables were evaluated using SSTDR and FDR methods to detect and locate electrical cable exposure to water. Both SSTDR and FDR showed the presence of water with a non-shielded cable. Moisture was only detectable with the shielded cable if the insulation was damaged.

reflectometry cable test, cable moisture detection↗

DOE OSTI2023

Spread Spectrum Time Domain Reflectometry (SSTDR) and Frequency Domain Reflectometry (FDR) for Detection of Cable Anomalies Using Machine Learning

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

Spread spectrum time domain reflectometry (SSTDR) and frequency domain reflectometry (FDR) cable inspection using machine learning

Cables are initially qualified for nuclear power plant use for 40 years. As plants extend their operating license to 60 and 80 years, justification for continued cable use must shift to a condition-based approach since it is cost prohibitive to completely replace cables that are likely still capable of performing their design function. The Pacific Northwest National Laboratory (PNNL) Accelerated and Real Time Experimental Nodal Analysis (ARENA) cable motor test bed was used to test the response of a commercial spread spectrum time domain reflectometry (SSTDR) system, a laboratory instrument software-controlled SSTDR, and a vector network analyzer-based frequency domain reflectometry (FDR) system to various cable anomalies. The three instrument systems were able to interrogate cables over a range of frequency bandwidths that can be helpful for human data analysis. Data were subjected to supervised and unsupervised machine learning (ML) analyses to distinguish normal undamaged cable responses from anomalous cable responses. Both supervised and unsupervised ML approaches produced encouraging results with an undamaged/anomalous prediction accuracy from 0.69% to 0.87%. Recommendations for further development and field implementation include increased and more balanced sample sets particularly including more training data.

SSTDR, FDR, Reflectometry, Machine Learning, ARENA↗

DOE OSTI2023

Spread Spectrum Time Domain Reflectometry (SSTDR) and Frequency Domain Reflectometry (FDR) for Detection of Cable Anomalies Using Machine Learning

Cables are initially qualified for nuclear power plant use for 40 years. As plants extend their operating license to 60 and 80 years, continued use of these cables must shift to a performance-based approach since it is cost prohibitive to completely replace cables that are likely still capable of performing their design function. A variety of cable tests are available and are commonly applied during outages when the cables can be taken out of service. Frequency domain reflectometry (FDR) is one of these test methods that is being more broadly accepted and used because it not only detects anomalies along the cable with a low-voltage signal that does not stress the cable insulation, but the technique also locates the anomalies. This supports follow-up local inspection and local repair or partial replacement of a damaged cable segment. Currently, FDR testing is only applied to cables that are taken out of service since the test instrument would be damaged by operational voltages. A related technology that has found some acceptance in the aircraft and rail industry is spread spectrum time domain reflectometry (SSTDR). This technology has been implemented with a custom commercial instrument by LiveWire Innovation Inc. that is designed to operate on live cables up to 1000 volts. One of the main conclusions of a previous effort was that cable reflectometry plots can be difficult for humans to analyze due to baseline noise, low or noisy anomaly response peaks, or large responses from cable ends. Detection of cable anomalies for many of these frequencies and test conditions was challenging for manual analysis. This presented an ideal opportunity for ML analysis to distinguish undamaged cable indications from anomalous cable indications. This research discusses application of machine learning (ML) to reflectometry cable test methods. The goal was to assess feasibility to distinguish undamaged cable reflectometry responses from damaged or anomalous cable reflectometry responses. The assessment considered the 3 instruments, multiple frequency bandwidths from each instrument, multiple cable anomalies and test conditions, and both supervised and unsupervised ML approaches. Although approaches and analysis methods were not identical or directly comparable, both outputs were encouraging. The unsupervised prediction weighted accuracy was assessed by instrument and by frequency. It performed better at high frequencies with the highest prediction accuracy of 0.84 for the higher frequency FDR, 0.79 for the 48-MHz LiveWire SSTDR, and 0.77 for 300-MHz PNNL SSTDR. The initial weighted accuracy average across all frequencies for using supervised ML was 0.56 to 0.68. The supervised analysis was repeated with noisier training data removed resulting in weighted accuracies of 0.69 to 0.87. These weighted accuracies are not directly comparable due to differences in the supervised and unsupervised analysis details but do indicate an encouraging trend. Even with limited and unbalanced data, strong prediction accuracies seem encouraging for further work including more data under a wider range of conditions.

42 ENGINEERING↗

DOE OSTI2024

Minimization of Measurement Uncertainty in Optical Frequency Domain Reflectometry

Optical frequency domain reflectometry (OFDR) is a technique for interrogating optical fiber sensors to generate relative, quasi-distributed measurements. Although Optical frequency domain reflectometry (OFDR) is increasingly being adopted for aerospace, energy production, and structural monitoring applications, the quantification of uncertainty for OFDR measurements has not been developed beyond sparse empirical relationships. To address this knowledge gap, an uncertainty metric for OFDR measurements was developed. This uncertainty metric was applied to weight the edges between OFDR measurements on directed correlation graphs and analyzed to minimize the cumulative uncertainty. In conclusion, this work is the first to propose an uncertainty metric for OFDR and provides a generalized mathematical framework for optimizing OFDR hardware selection, optical fiber sensor selection, and postprocessing strategy.

42 ENGINEERING↗

DOE OSTI2021

Full-Wave and Circuit-Based Simulations of Cable Insulation Aging/Damage Using Time-Frequency Domain Reflectometry

This paper presents a combined full-wave and circuit-based simulation study to investigate the important topic of cable insulation aging and physical damage. The analysis employs the time-frequency domain reflectometry (TFDR) technique that combines the advantages of both time domain reflectometry (TDR) and frequency domain reflectometry (FDR) for improved location identification and feature resolution. Coaxial cable sections with a location containing insulation aging or physical damage are simulated using Ansys High Frequency Structure Simulator (HFSS). Simulated scattering (S) parameters are then imported into the Advanced Design System (ADS) solver for time domain simulation where a Gaussian windowed chirp signal or ‘chirplet’ is launched. Finally, continuous wavelet transform (CWT) is applied in MATLAB to perform time-frequency analysis of the reflected waveforms. The results reveal that a small change in the relative permittivity of the insulation or the presence of a small point of physical damage on the insulation is reflected as a considerable change in the CWT magnitude demonstrating the efficacy of the method.

cable aging, Non Destructive Examination, time-fre↗

DOE OSTI2023

Effect of Measurement Temperature on Electrical Cable Frequency Domain Reflectometry Response

In nuclear power plants, electrical cables are exposed to stressors, such as elevated temperature and radiation. Evaluation of the effect of stressors on the lifetime of electrical cables can be conducted using offline electrical reflectometry techniques, such as frequency domain reflectometry (FDR). However, recent work has raised the concern that FDR measurements at temperatures higher than ambient may diminish or reduce the response due to stressors, potentially leading to incorrect predictions of electrical cable damage and lifetime. In this work, we explore the FDR response of an electrical cable exposed to an oven-based thermal stressor up to 140°C, including both ramping up and ramping down temperature. It was observed that, for both the oven entrance and exit, an increase in the FDR measurement temperature led to a decrease in the FDR reflection coefficient. In particular, it was found that the reflection coefficient at the oven entrance decreased from the ambient measurement by approximately 7%, 22%, and 36% at a temperature of 60°C, 100°C, and 140°C, respectively.

Spencer, Mychal P.↗

DOE OSTI2022

Nondestructive Evaluation (NDE) of Cable Anomalies using Frequency Domain Reflectometry (FDR) and Spread Spectrum Time Domain Reflectometry (SSTDR)

This report presents a comparative assessment of the performance of frequency domain reflectometry (FDR) and spread spectrum time domain reflectometry (SSTDR) in detecting a wide range of electrical cable anomalies. All tests and results reported herein were performed at the PNNL Accelerated and Real-Time Environmental Nodal Assessment (ARENA) cable and motor test bed. The primary objective of this work was to evaluate the effectiveness of SSTDR, a fledgling cable monitoring technique that shows promise for application in online monitoring of energized cable systems, against FDR, an offline technique widely employed in the nuclear power plant (NPP) industry. FDR tests are becoming more widely used in nuclear power plant cable aging management and test programs – particularly for low voltage cables. FDR capabilities for these kinds of tests have been reported by PNNL and others. The FDR test is performed on de-energized cables by connecting the FDR instrument to two of the cable conductors, or one conductor and the shield. A broad band low voltage (< 5 V) chirp is introduced in the cable, and any reflected response is captured in the frequency domain. The captured reflection is then processed by performing an inverse Fourier transform to a time domain response which can then be converted to a distance response based on the cable velocity of propagation (VoP). SSTDR measurements are functionally similar to FDR measurements in that a broad-band voltage signal composed of a square or sine wave modulated pseudo-random sequence of chips (< 5 volts), is injected onto one of the cable conductors. The injected signal will experience partial energy reflection and transmission at each impedance discontinuity along the transmission line. Any reflected response is detected by computing a cross-correlation between the reflected signals and a delayed copy of the incident SSTDR signal. the time delay for the reflected signal to experience the best matched correlation with the incident signal, indicates the travel time for the signal to reach a change in impedance. By knowing this time delay and velocity of propagation (VoP) of the signal, one can compute the physical distance. A big advantage that SSTDR measurements have over other methods is the ability to be connected to energized or live wires (currently up to 1kV) thereby enabling online monitoring of cables. SSTDR has been used successfully in several applications, e.g., aircraft, rail, and photovoltaic systems. In this work FDR and SSTDR cable assessment techniques were used to characterize a variety of cable anomalies and faults including: (1) Presence or absence of a motor; (2) Ground faults and short circuit faults; (3) Moist environments and water ingress faults; (4) Accelerated thermal aging. Both shielded and non-shielded cables were evaluated in this report. Offline measurements were made using FDR and online measurements were made by SSTDR for a range of test scenarios. Based on the results across all cable anomalies evaluated in this study, FDR displayed high sensitivity towards cable condition assessment, while SSTDR showed promise for future application in monitoring NPP cable systems. However, further developments are suggested to improve the resolution and sensitivity of SSTDR towards faults and anomalies in low voltage cables.rt presents a comparative

42 ENGINEERING↗

DOE OSTI2023

Frequency Domain Reflectometry (FDR) Simulation Techniques for Digital Twin Representation of an Electrical Cable

Simulation of cable system response to frequency domain reflectometry (FDR) tests can be instrumental to understanding these tests and the nature and influence of various cable anomalies on test signatures. Reflectometry simulations are based upon a finite element representation of cable conductors and insulation to produce an S-parameter at each evaluated frequency. The aggregate collection of cable model S-parameters can simulate the influence on a test signal injected into a physical cable. Such an approach was undertaken in this work to produce a digital twin simulation of a low-voltage electrical cable. The electrical cable digital twin examined the influence of test simulation parameters and the relative influence of cable anomalies, including thermal aging, water or moisture exposure, water or moisture ingress, and other anomalies. The digital twin in this work included modeling of the conductors, insulation, jacket, and surrounding environment (air, water, etc.). The digital twin could be expanded to include cable bends, junctions and splices, branch or T systems, and termination impedances of motors or instruments. Observations and conclusions of this work include: 1. Fully 3D digital twin simulation of an electrical cable using an FDR approach is possible. However, there are tradeoffs between simulation fidelity and solution time, which must be balanced to ensure the simulation solves in an adequate amount of time (e.g., less than 20 minutes). Simulation parameters to balance include frequency bandwidth, number of frequencies, mesh density, connection impedance, and permittivity tolerance. 2. The digital twin simulation can explain FDR sensitivity to various cable anomalies, including entry and exit from an oven or water bath. 3. The digital twin simulation FDR response attenuates with distance along the cable and is further affected by the frequency bandwidth, which is similar to that observed with physical measurements. 4. The resolution of the digital twin FDR peaks increased with increasing bandwidth and with increasing number of frequencies, again similar to physical measurements. 5. The presence of multiple anomalies in the digital twin does not substantially attenuate the FDR response to anomalies located beyond the first encountered anomaly and impedance mismatch. 6. Spectral variation of the permittivity did not have a significant effect on the FDR response compared to a fixed nominal value. 7. Extension of the digital twin to 1000 ft still allowed for detection of distal anomalies near the far end of the electrical cable from the instrument connection point. 8. The ARENA test bed facilitates efficient NDE evaluations of well understood cable anomalies with various NDE methods without risking actual plant damage.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

3D Frequency Domain Reflectometry Digital Twin of an Electrical Cable: A First Glance

Electrical cables within nuclear power plants (NPPs) are critical components required for power, control, and instrumentation systems which may be exposed to stressors, such as elevated temperatures and gamma radiation. Such stressors can lead to a reduction in the remaining useful life of electrical cables, jeopardizing the safety of NPP systems. To evaluate the effect of stressors on the degradation of electrical cables, electrical reflectometry methods are commonly employed. Frequency domain reflectometry (FDR) is a non-destructive electrical reflectometry method that uses transmission line theory to detect degradation or impedance changes within electrical cables. However, in most cases FDR is only applied to de-energized cables, limiting the application in NPPs as the cable system must be taken offline. In this work, we explore the development of an FDR digital twin to predict the degradation of an electrical cable exposed to elevated temperature, which is expected to reduce the need for offline FDR. A 3-conductor low-voltage electrical cable was selected for evaluation of the digital twin. The fully three-dimensional digital twin was developed in COMSOL using the RF module. A cable length of 30-m and frequency bandwidth of 400 MHz was selected to mimic real-world application of FDR. Over a 1-m region, the permittivity of the insulation was varied by up to 20% to model thermal degradation. The results demonstrate accurate detection of the insulation damage region, supporting further investigation of the FDR digital twin using real-world data and machine learning for predictive damage estimation or remaining lifetime.

Spencer, Mychal P.↗

DOE OSTI2021

Nondestructive Evaluation (NDE) of Cable Moisture Exposure using Frequency Domain Reflectometry (FDR)

This Pacific Northwest National Laboratory (PNNL) milestone report assesses the capability of frequency domain reflectometry (FDR) to determine electrical cable submergence using PNNL’s Accelerated and Real-Time Environmental Nodal Assessment (ARENA) cable/motor test bed. This work includes a review of relevant literature as well as experimental tests. Nuclear power facilities have experienced various electrical cable failures related to water exposure. The current industry response involves actions to de-water cable vaults, manholes, and other cable locations. These efforts require considerable expenditure of resources, which makes it desirable for the industry to have information on cable condition and history regarding their submergence and water exposure (Mantey 2012). Two tests that are gaining favor within the nuclear industry are time-domain reflectometry (TDR) and FDR. These are low-voltage nondestructive tests that can be applied at a cable end. Testing from the cable end is important because local inspection along the cable length is very difficult due to cables being routed within trays, conduits, underground, and through walls. Both TDR and FDR techniques have been shown to locate cable insulation damage due to thermal, radiation, and mechanical damage. FDR measurements are also more sensitive than TDR to temperature changes, low-bend radius bends, and cable contact with various materials, including conductive materials like steel and water. This work evaluates the feasibility to extend FDR testing to characterizing whether an electrical cable is submerged or not and where it may be submerged using PNNL’s ARENA cable/motor test bed.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

Quasi-Extended Range Optical Frequency Domain Reflectometry for Product Pipelines

Throughout the United States, large natural gas and product transmission pipelines exist. These pipelines are susceptible to failure through corrosion and cracking due to internal and external factors. As these transmission pipeline age, the likelihood of a catastrophic failure increases. The ability to the monitor corrosion and wall thickness of these pipelines is paramount to reduce risk of disastrous failure and increase reliability as well as safety. Optical frequency domain reflectometry can monitor distributed temperature and strain measurements along the natural gas and product pipelines. This measurement technique can provide valuable information of pipe structural health through hoop strain changes due to pipe wall thinning, temperature changes due to gas leaks based on Joule-Thomson effect. Since these pipelines are typically buried, the depth of the pipeline results in a potential loss in the sensing range where the fiber is not physically monitoring the hoop strain of the pipeline. A different configuration of the interferometer will allow for the distributed fiber measurement to start atop the pipeline itself. This configuration results in no loss of sensing range and maintains the sensing resolution of a typically interferometer for an optical frequency domain reflectometry measurement. The quasi-extended range distributed hoop strain measurements were demonstrated on an active transmission pipeline.

Brister, Matthew↗

NASA NTRS2016

Remote Strain Sensing of CFRP Using Microwave Frequency Domain Reflectometry

NASA's Advanced Composites Project is investigating technologies that increase automated remote inspection of aircraft composite structures. Therefore, microwave Frequency Domain Reflectometry (FDR) is being investigated as a method of enabling rapid remote measurement of strain occurring at the first ply of a composite fiber reinforced polymer (CFRP) structure using Radio Frequency (RF) Electro-Magnetic (EM) radiation. While microwave reflectometry has been used to detect disbonds in CFRP structures, its use in detecting strain has been limited. This work will present data demonstrating the measurement of the reactance changes due to loading conditions that are indicative of strain in a CFRP structure. In addition, the basic EM signature will be presented along with an analysis of temperature and humidity effects.

Wilson, William C.↗

NASA NTRS2023

Basic Theory and Operating Principles of Optical Frequency Domain Reflectometry Measurement Systems as Applied to Fiber Bragg Grating Sensors

Optical frequency domain reflectometer (OFDR) systems provide for the interrogation of hundreds of fiber Bragg gratings (FBGs) within a single optical fiber. The coupling of FBG sensors to an OFDR interrogator results in a highly distributed measurement system utilizing sensors that are lightweight, immune to electromagnetic interference, and low-profile. This paper presents and explores a basic derivation of OFDR-FBG signals, the processing of those signals, the assembly of a basic OFDR system, an example measurement scenario, and the effects of specific component and configuration changes on interrogator speed, resolution, and accuracy.

optical frequency domain reflectometry↗

DOE OSTI2023

Online Monitoring of Medium Voltage Cable Systems with Spread Spectrum Time Domain and Frequency Domain Reflectometry

In-service failures of wave energy convertor (WEC) cable systems can have a significant cost and power availability impact. Close parallel research 2019 data showed > 1B£ and 9 Terra-Watt-Hours associated with global off-shore wind (OSW) cable failures (Strang-Moran 2020). OSW is a closely related technology but currently is significantly cheaper than WEC technology. For wave energy to compete, the problem of reliable cable transmission must be mitigated. This project develops isolation technology to allow online high frequency reflectometry testing of medium voltage cables (1 to 10 kV and higher) without arcing or damage to the test instrument. Online spread spectrum time domain reflectometry (SSTDR) testing has been established for low voltage cable systems in the aircraft and rail industry and the ability to detect and locate cable flaws of interest is well understood. Extending reflectometry testing to medium voltage systems could enable detection of cable damage before failures occur thereby allowing repair and replacement of damaged cable segments to be scheduled and managed. The seedling project succeeded to pass and receive high frequency SSTDR signals onto a cable up to 1 kV using a parallel trace isolation circuit board that can be connected onto the test cable. The approach used a novel circuit design for which an invention disclosure has been filed. A proposed sapling project would extend the technology toward the higher operating voltages used by WEC systems, thereby enabling online SSTDR cable monitoring. The goal of the seedling project was to extend the capability of the ARENA cable/motor test bed to address medium voltages and to develop a high pass filter isolation architecture to protect the reflectometry instrument from the low frequency (DC – 60 Hz) line voltage while allowing the high frequency diagnostic signal to pass to and from the test instrument to the live line. Initial efforts focused on passive LCR filter circuits to reduce 60 Hz levels below 10 volts from a 10 kV line while allowing the MHz high frequency chirps to pass onto the cables and for mV signals to be detected. We discovered that the parasitic loss behavior of real high voltage components precluded this approach from working. An alternate approach was adapted for the electric field to couple between two parallel traces on a printed circuit board much like a radio-frequency coupler. The challenge here was and is to have the parallel traces close enough to each other to effectively pass the high frequency chirp onto the live line and receive any reflected signal from any encountered impedance change along the cable. This reflected signal will be in the mV range. The traces however must be far enough apart to not allow arcing on the board. A design with 3 mm spacing was determined to allow the high frequency signal to pass onto the live line and receive the mV signal back into the instrument while reducing the 60 Hz voltage amplitude by >80 dB (more than a factor of 10,000) without allowing arcing from across the parallel traces. This was confirmed by simulation and test.

16 TIDAL AND WAVE POWER↗

NASA NTRS2014

Method and Apparatus of Multiplexing and Acquiring Data from Multiple Optical Fibers Using a Single Data Channel of an Optical Frequency-Domain Reflectometry (OFDR) System

A method and system for multiplexing a network of parallel fiber Bragg grating (FBG) sensor-fibers to a single acquisition channel of a closed Michelson interferometer system via a fiber splitter by distinguishing each branch of fiber sensors in the spatial domain. On each branch of the splitter, the fibers have a specific pre-determined length, effectively separating each branch of fiber sensors spatially. In the spatial domain the fiber branches are seen as part of one acquisition channel on the interrogation system. However, the FBG-reference arm beat frequency information for each fiber is retained. Since the beat frequency is generated between the reference arm, the effective fiber length of each successive branch includes the entire length of the preceding branch. The multiple branches are seen as one fiber having three segments where the segments can be resolved. This greatly simplifies optical, electronic and computational complexity, and is especially suited for use in multiplexed or branched OFS networks for SHM of large and/or distributed structures which need a lot of measurement points.

Parker, Jr., Allen R↗

DOE OSTI2024

Evaluation of Clamshell Current Coupler for Online Frequency Domain and Spread Spectrum Time Domain Reflectometry to Detect Anomalies in Energized Cables

This document describes adaptation and evaluation of a clamshell inductive current coupler for online reflectometry testing (both frequency domain reflectometry and spread spectrum time domain reflectometry) to evaluate cable insulation degradation and anomalies. Safety-critical nuclear power plant cables were initially qualified for 40 years. However, as plants extend their operating licenses to 60 and 80 years, justification for continued safe operation includes test and monitoring programs. These will become more important as the industry moves to condition based qualification programs. Cable test programs traditionally involve manual interventions to disconnect cables, perform one or several tests, then reconnect the systems, usually during refueling outages occurring only every 18 to 24 months. This poses an operational burden that can be minimized by online testing or periodic connection to a coupler that may remain on the cable of interest or be clamped onto the cable without de-termination. This work investigates the adaptation of a clamshell inductive current coupler for either frequency domain reflectometry or spread-spectrum time domain reflectometry. The reflectometry test instrument injects a broad-band chirp or pseudo-noise signal onto a cable conductor and monitors for a reflected signal indicative of an impedance change caused by a damage condition. The instrument maximum input signal levels are typically 10 to 30 volts or less and the instruments will be damaged if subjected to 60 Hz power line voltages of 110, 220, or 480 VAC. One commercial spread-spectrum time domain reflectometry system has circuitry suitable for voltages up to 1 kV, but typical reflectometry tests are performed on de-energized cables. The clamshell inductive coupler provides >60 dB of 60 Hz attenuation with less than 10 dB loss in the 1-500 MHz test bandwidth of interest. An energized cable was successfully tested up to 6.7 kVp-p and frequency response plots imply that the tests could be extended to 10 kV or higher energized levels.

36 MATERIALS SCIENCE↗

NASA NTRS2012

Algorithms for Determining Physical Responses of Structures Under Load

Ultra-efficient real-time structural monitoring algorithms have been developed to provide extensive information about the physical response of structures under load. These algorithms are driven by actual strain data to measure accurately local strains at multiple locations on the surface of a structure. Through a single point load calibration test, these structural strains are then used to calculate key physical properties of the structure at each measurement location. Such properties include the structure s flexural rigidity (the product of the structure's modulus of elasticity, and its moment of inertia) and the section modulus (the moment of inertia divided by the structure s half-depth). The resulting structural properties at each location can be used to determine the structure s bending moment, shear, and structural loads in real time while the structure is in service. The amount of structural information can be maximized through the use of highly multiplexed fiber Bragg grating technology using optical time domain reflectometry and optical frequency domain reflectometry, which can provide a local strain measurement every 10 mm on a single hair-sized optical fiber. Since local strain is used as input to the algorithms, this system serves multiple purposes of measuring strains and displacements, as well as determining structural bending moment, shear, and loads for assessing real-time structural health. The first step is to install a series of strain sensors on the structure s surface in such a way as to measure bending strains at desired locations. The next step is to perform a simple ground test calibration. For a beam of length l (see example), discretized into n sections and subjected to a tip load of P that places the beam in bending, the flexural rigidity of the beam can be experimentally determined at each measurement location x. The bending moment at each station can then be determined for any general set of loads applied during operation.

Richards, W. Lance↗