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Korompili, G.; Mußbach, G.; Riziotis, C. Structural Health Monitoring of Solid Rocket Motors. Encyclopedia. Available online: (accessed on 21 April 2024).
Korompili G, Mußbach G, Riziotis C. Structural Health Monitoring of Solid Rocket Motors. Encyclopedia. Available at: Accessed April 21, 2024.
Korompili, Georgia, Günter Mußbach, Christos Riziotis. "Structural Health Monitoring of Solid Rocket Motors" Encyclopedia, (accessed April 21, 2024).
Korompili, G., Mußbach, G., & Riziotis, C. (2024, March 12). Structural Health Monitoring of Solid Rocket Motors. In Encyclopedia.
Korompili, Georgia, et al. "Structural Health Monitoring of Solid Rocket Motors." Encyclopedia. Web. 12 March, 2024.
Structural Health Monitoring of Solid Rocket Motors

In the realm of space exploration, solid rocket motors (SRMs) play a pivotal role due to their reliability and high thrust-to-weight ratio. Serving as boosters in space launch vehicles and employed in military systems, and other critical & emerging applications, SRMs’ structural integrity monitoring, is of paramount importance. Traditional maintenance approaches often prove inefficient, leading to either unnecessary interventions or unexpected failures. Condition-based maintenance (CBM) emerges as a transformative strategy, incorporating advanced sensing technologies and predictive analytics. By continuously monitoring crucial parameters such as temperature, pressure, and strain, CBM enables real-time analysis, ensuring timely intervention upon detecting anomalies, thereby optimizing SRM lifecycle management. Particularly, photonic sensors and fiber-optic sensors, demonstrate exceptional promise in CBM goals. Their enhanced sensitivity and broad measurement range allow for capturing subtle changes indicative of degradation or potential failures. These sensors enable comprehensive, non-intrusive monitoring of multiple SRM locations simultaneously. Integrated with data analytics, these sensors empower predictive analysis, facilitating SRM behavior prediction and optimal maintenance planning. Ultimately, CBM, bolstered by advanced photonic sensors, promises enhanced operational availability, reduced costs, improved safety, and efficient resource allocation in SRM applications.

solid rocket motors condition-based maintenance structural health monitoring Sensors Optical  fibers Defect detection Machine learning

1. Traditional Maintenance Practices: Destructive Testing

Currently, the condition of SRMs is investigated by periodical destructive testing [1] performed on a limited number of SRMs, which is considered representative of a certain typical population. Particularly, the motors are separated from the missile and dissected, the charge specimens are extracted by milling and cutting [2], and chemical and mechanical analysis of the specimens is performed to determine the aging state of the material and compare it with limiting values derived from qualification and structural analysis. Destructive testing includes visual inspection of the components of the SRM [1], which is the most basic form of inspection and involves looking for signs of defects on the surface of the SRM, such as cracks, bulges, or discoloration. Visual inspection is often assisted by several imaging techniques and appropriate instrumentation. The destructive testing also includes a series of experimental processes, among which the most frequent is thermal cycling. Thermal cycling tests expose the SRM to rapid and repetitive temperature variations, simulating the thermal stresses experienced during launch and atmospheric reentry [3]. By subjecting the motor to extreme temperature differentials, engineers can assess its ability to withstand thermal gradients, evaluate material fatigue, and detect potential weaknesses in the insulation and structural components. Additional processes may involve overpressurization tests, subjecting the SRM to pressures exceeding its nominal operating range [4], and static test firing, which refers to the ignition of the SRM in a controlled environment to simulate operational conditions. Pressure tests help in the identification of the SRM’s structural limits and the observation of failure mechanisms such as rupture, debonding, delamination, or buckling [5]. Static test firing allows for the measurement of thrust, chamber pressure, and burn rate, providing information on the motor’s performance and enabling the validation of design predictions [6].
In general, destructive testing processes are assisted by strain gauges, which are used to measure structural deformation and stress distribution during destructive testing, and high-speed imaging digital cameras or video recorders, which capture the dynamic behavior of the SRM during testing.
Destructive testing is an expensive, tedious, and time-consuming process, providing results with a considerable delay [7], when additional aging may have taken place. Moreover, it cannot guarantee the detection of every potential problem or failure scenario, as it is performed on a limited number of samples considered representative of a specific SRM population [8]. Additional measures, such as statistical analysis, modeling, and simulation, are at least indispensable to expand the test results to the broader population. Still, variations in manufacturing processes, material properties, or environmental conditions can result in unique challenges in life-expectancy predictions or failure mechanisms that may not be fully captured, leading to unreliable predictions—depending on specific samples—in the condition and life expectancy of a high number of SRMs.

2. Non Destructive Testing: Imaging Approaches

The limitations of destructive testing have led to the development of various nondestructive testing approaches that can provide valuable information for defect detection, characterization, and assessment, facilitating proactive maintenance and preventing catastrophic failures.
In general, imaging approaches present limitations in terms of inspection depth, sensitivity to certain defect types, or limited access to certain areas of SRMs. As nondestructive imaging techniques evolved, each method introduced unique capabilities and limitations. Ultrasonic testing (UT) provided valuable insights into internal structures but had challenges in detecting surface defects. X-ray inspection and computed tomography (CT) imaging offered comprehensive internal views but were limited in surface defect detection [9]. Magnetic particle inspection excelled in surface flaw identification but struggled with subsurface defects. Acoustic emission testing provided real-time monitoring but had challenges pinpointing specific defect locations. Thermography proved effective for surface defects but lacked precision and in-depth assessment, and digital image correlation (DIC) offered full-field deformation data but was not designed for subsurface defect detection. Each method’s limitations were often complemented by the strengths of others. For a comprehensive evaluation, integrating multiple techniques became essential, ensuring a thorough assessment of solid rocket motor components by overcoming individual limitations.

3. Sensing Approaches for the SHM of SRMs

3.1. Strain Gauges and DBST Sensors

Strain gauges are sensors that can be attached to an SRM to measure deformation of the material to which they are attached and translate it to the corresponding changes in strain or stress [10]. These measurements can be used to identify areas of the SRM that are under excessive stress, which may indicate the presence of defects. Dual bond stress and temperature (DBST) sensors are specifically designed for health monitoring of SRMs [11]. They measure both radial stress (bond stress) and temperature at their active surface near the case wall simultaneously during manufacturing and thermal cycling. DBSTs are embedded in the motor against the inner case wall during the manufacturing process and can use wired or wireless technologies to obtain data [12].
The use of multiple sensors—at least three—placed in the circumferential direction of the SRM cross-section, at the midplane of the motor, can assure the detection and localization of bore cracks and debonding in the vicinity of that cross-section [11][13]. DBST sensors have also been used to determine the effects of aging on the propellant modulus and stress-free temperature by slowly heating and cooling the motor while measuring stress at various temperature plateaus [14].

3.2. Piezoelectric Sensors

Piezoelectric sensors play a pivotal role in the field of structural health monitoring (SHM), not only in the context of solid rocket motors but also in various other sensing applications [15]. These sensors are based on the piezoelectric effect, which allows certain materials, such as piezoelectric crystals or polymers, to generate electric charges when subjected to mechanical stress or deformation. In SHM, piezoelectric sensors are strategically placed within structures, such as solid rocket motors, to monitor their mechanical integrity over time. When structural defects or changes occur, they induce mechanical stress or vibrations, which are promptly detected by the embedded sensors. The resulting electric charges are then converted into measurable signals, enabling real-time monitoring of the structure’s health. This technology is invaluable for the early detection of defects, cracks, or anomalies, allowing for preventive maintenance or timely intervention to avert catastrophic failures. Piezoelectric sensors offer a noninvasive, highly sensitive, and efficient means of monitoring structural health in a wide range of applications, ensuring the safety and reliability of critical systems.
More precisely, a piezo film (ceramic or polymer) has been developed and positioned between conductive plates in the form of a “sandwich” that is protected by polyester laminates [16]. Experiments conducted at room temperature on propellant during the curing phase using an embedded piezoelectric PVDF-based sensor showed a reduction in capacitance of 35 pF during the initial 6 days of curing [16]. This reduction in capacitance serves as an indicator of changes in the propellant’s modulus and provides valuable information for monitoring the curing process and the structural health of the propellant. However, the long-term monitoring of propellant health is not addressed. Additionally, the corresponding study do not delve into the practical challenges and complexities associated with implementing a remote data acquisition system for multiple sensors in a full-scale motor, which is crucial for real-world applications. The efficiency of this type of sensor also depends on the sensors’ position, which is tightly related to the purpose of their use. To determine the modulus, the sensors are placed in a low-stress area (e.g., far from the bulb tip stress reliefs), while damage detection implies the positioning of sensors in areas where flaws are expected to appear (i.e., the propellant liner interface). An alternative architecture of piezoelectric capacitance device was proposed and demonstrated [17] where one or multiple sensors could be embedded in the SRM’s energetic propellant material.
Despite their benefits, piezoelectric sensors also come with certain limitations and drawbacks. The surface charge produced by an applied force in a piezoelectric sensor can be affected by various factors, including charges from the environment (airborne charges), current leakage due to the nonzero conductivity of the dielectric material, or the input resistance of the connected electronics. These factors can collectively act as a high-pass filter for input signals, which can make it challenging to use piezoelectric sensors for pure static measurements [18]. Additionally, their sensitivity to environmental factors such as temperature can be a drawback. This is due to the fact that changes in temperature can affect the piezoelectric material’s properties, potentially leading to false readings or requiring complex compensation techniques. The temperature fluctuations can induce crystal deformation within the sensor, leading to an electrical output. If different components of the sensor, such as clamping parts and electrodes, have different thermal expansion coefficients, it can result in the crystal experiencing unintended mechanical forces, further affecting the sensor’s performance [18]. While the piezoceramic films are very effective and thermally stable, they often have a poor mechanical impedance match with certain materials, such as propellants, and they tend to be brittle, which can be a limitation in applications where flexibility or durability is required. On the other hand, piezoelectric polymer films (e.g., PVDF, polyvinylidene fluoride) offer better impedance matching with materials such as propellants, and they are flexible, allowing for versatile use, but they have poor thermal stability, rendering them suitable for high-temperature environments. Finally, piezoelectric sensors are susceptible to electromagnetic interference, which can introduce noise into the collected data [19]. Their installation can be challenging in some structures, especially those with irregular shapes or limited access points. Maintaining a reliable electrical connection over extended periods can also be a concern.

4. Photonic Sensing Approaches: Towards CBM of SRMs

4.1. Interferometric Sensors

Interferometric sensors have emerged as a groundbreaking technology in the field of SHMs for aerospace composites, enabling precise and comprehensive assessment of their integrity [20]. Operating on the principle of interference, these sensors utilize advanced optical techniques, such as fiber-optic interferometry, to measure infinitesimal changes in the environment they are embedded within [21]. A distinct case of interferometric-based sensors could be laser Doppler vibrometers (LDVs) [22] for remote monitoring of vibrations. Although their operation is entirely different from that of waveguide-based interferometers and other fiber-optic sensors considered here, they offer the advantages of easier or seamless integration and real-time monitoring [23]. By employing interferometric sensors, engineers can monitor distributed strain, temperature variations, and other critical parameters along the entire length of the solid rocket motor. The most common type of interferometric sensors used in SHM are fiber-optic interferometers (FOI), which can be also classified as intrinsic or extrinsic depending on the design of the cavity and the corresponding sensors’ footprint. Such interferometric sensors have been based in various architectures utilizing also Bragg gratings [23], long-period gratings (LPGs) [24], and photonic crystal fibers (PCFs) [25]. The key advantage of interferometric sensors lies in their remarkable resolution, which can exceed 1 µε for strain measurement. Worth noting that early applications of fiber-optic sensors in SHM, pioneered by McDonnell Douglas in the 1980s, employed the Sagnac interferometer as a strain sensor [26].
Among the most common types of FOI are Fabry-Perot interferometers (FPIs), which consist of two reflective surfaces separated by a small gap. Changes in the gap distance due to structural deformations or temperature fluctuations lead to alterations in interference patterns [27]. FPI sensors boast resolutions as high as 0.15 µε and a broad measurement range from −5000 µε to +5000 µε. These sensors are compact, ranging from 1 to 20 mm in length, allowing seamless integration into structures without significantly impacting their mechanical properties. They can withstand temperatures of up to 250 °C; however, their limited multiplexing capability restricts their application to a relatively small number of measurement points [28]. FPI sensors offer high accuracy, versatility, and the ability to measure both static and dynamic strains, making them suitable for real-time monitoring of SRM components during ignition and flight.
Fiber-optic Mach-Zehnder-based interferometers (MZIs) have also been implemented and employed for the study of intrachamber processes in SRMs [29]. In this experimental study of a model solid propellant rocket motor, noninvasive control with MZI fiber-optic sensors enabled monitoring of the burning rate of solid propellant. The results revealed the feasibility of noninvasive control by recording combustion front arrival time and analyzing spectrogram peaks, providing insights into the combustion chamber’s longitudinal modes and confirming a nearly constant combustion rate [29].
Michelson interferometers split incoming light into multiple paths, allowing for the detection of phase shifts caused by mechanical vibrations, temperature changes, or structural deformations. While they provide high sensitivity and precision, Michelson interferometers may require complex optical setups and alignment procedures and are more complex compared to MZI architectures [30]. Despite the inherent high sensitivity of FOIs, their main limitation is the lack of scalability in a single fiber. As a result, it is not easy to integrate multiple sensors in a fiber, limiting the capabilities for multipoint or distributed sensing. The interrogation unit of such FOIs is also quite complex, with high costs and multiple interrogators needed for multiple FOIs, increasing overall installation costs.

4.2. Intensity-Based Fiber-Optic Sensors

A much simpler fiber-optic configuration applied in SRM’s propellant monitoring is pristine optical fibers employing a simple amplitude interrogation unit. Different types of polymer optical fibers (POFs), including both jacketed and unjacketed types, were embedded in propellant specimens using specialized primer and glue that assured an excellent bonding between fiber and propellant. The high elasticity (low Young’s modulus) of such polymer optical fibers [31] allowed for the consistent transfer of propellant stress or strain behavior into the embedded fiber, which responded accordingly. These fibers were fabricated with a core made of PMMA and a cladding of fluorinated polymer. In their bare form, such typical multimode POFs with a core diameter of 980 μm and with a 10 μm-thick cladding layer that increased the total diameter to 1 mm were employed. while also jacketed types of fiber-optic cables, with a polyethylene or polyamide jacket, have also been employed. Two distinct fiber arrangements were utilized in previous studies: one involved a longitudinal orientation of the fiber within the propellant, parallel to the stretching direction, while the other incorporated a closed fiber loop. In the first arrangement, both unjacketed PMMA POF and polyamide jacketed POF responded consistently, closely mirroring the behavior of the sample even under excessive strains of up to 8% and 30%, respectively. This response was due to a decrease in transmitted light caused by higher optical propagation losses attributed to axial elongation. For the fiber loop arrangement, the unjacketed PMMA POF, through macro-bending induced optical losses, closely followed the applied force and elongation up to a strain value of 10% [32][33].
Intensity-based POF sensors [31] offer several advantages in the context of SHM for SRMs. They are relatively easy to embed within propellant specimens due to their small size and flexibility. Their construction from PMMA and fluorinated polymer grants them resistance to environmental factors typically present in rocket motor environments. Additionally, their ability to respond consistently to strain allows for accurate monitoring of structural changes [34] in the propellant material. POF sensors exhibit notable characteristics, including good stability, cost-effectiveness, and a substantial strain range of 60% [35]. In relevant studies, the findings emphasize the versatility of POFs in not only tracking the strain state of viscoelastic solids but also in identifying initial cracks and monitoring their propagation until reaching ultimate failure [35][36].

4.3. Fiber Bragg Gratings (FBGs)

In the realm of SHM and CBM for SRMs, FBG-based sensors have emerged as invaluable tools that could offer precise insights into the structural integrity and performance of these critical aerospace components. FBGs are fabricated by laser-inducing permanent periodic variations in the refractive index along an optical fiber, creating a wavelength-specific reflection. When subjected to strain, the spacing between these periodic variations changes and causes a shift in the reflected wavelength, which can be measured to accurately determine the strain experienced by the structure of the SRM, enabling precise strain or temperature monitoring. The way of enhancing SRM monitoring begins with single-mode silica optical fiber FBGs [37][38]. FBGs can be inscribed inside the core of the fiber in a continuous, seamless, nonintrusive way (by a laser-based writing process), providing the capability of fully customizing their optical properties and accommodating in a single fiber—theoretically—an infinite number of FBGs separated optically and spatially in a way to offer multipoint or distributed sensing over the entire fiber’s length. These sensors, embedded strategically within SRMs, provide high-resolution measurements of various parameters, such as strain and temperature. In one approach, FBG sensors made from ordinary quartz single-mode fibers, embedded in raw composite material, were employed to monitor the entire curing process, ranging from heating and insulation/curing to cooling, occurring between 20 °C and 140 °C [39]. The subtle shifts in wavelengths they record over time can provide not just insights but a roadmap into the curing degree of the propellant grain. This level of granularity is crucial for CBM, allowing engineers to gauge the exact state of the SRM at any given moment. These FBG sensors have exhibited remarkable sensitivity to both tensile and compressive stresses, making them effective tools for monitoring debonding tests where artificial defects were created, enabling the precise determination of debonding locations.
In another instance, FBG sensors, using polymer packaging, have been strategically placed to measure bond stress between the propellant and insulation during the curing, demolding, and debonding processes. These sensors, distributed along the circumference of the motor at the propellant/insulation interface, detected shifts in the FBG center wavelength, indicating variations in bond stress. The sensors were also subjected to axial and uniaxial tensile stresses, revealing significant stress gradients in the circumferential direction [40], which can be vital markers for CBM algorithms. They hint at areas of potential weakness, allowing for proactive maintenance measures before structural integrity is compromised. Additionally, simplified fiber filament wound scale SRM models have been created, incorporating FBG sensors in key locations within model shells. These sensors monitored the internal hydraulic pressure applied to simulate SRM shell casing working conditions, providing crucial data on circumferential and axial strains [41].
Moreover, an active sensing method utilizing FBG strain sensors has been discussed for monitoring solid propellant integrity. This method involves applying dynamic loads to a structure and observing resulting deformations. The active sensor, comprising a flexible ring with a Terfenol bar and Bragg grating sensor, provided valuable insights into the mechanical properties of SRM propellant grains [42]. The system’s ability to characterize these properties by measuring the amount of deflection due to applied loads demonstrated its potential for robust SHM in SRMs, in addition to further enabling the predictive analyses that form the cornerstone of CBM.
The use of silica optical fibers encounters certain limitations, notably related to their susceptibility to mechanical damage and challenging installation procedures [43]. It is important to note that the current limited practice in the integration of FBGs into the SRM structure lacks standardization, with high-temperature-resistant adhesives/primers or epoxy glues being necessary to assure precise strain or temperature measurement within SRMs. A notable advancement in FBG technology comes in the form of polymer optical fiber FBGs (POFBGs) [44]. These sensors, composed of polymer materials, offer enhanced flexibility and easier installation, addressing the fragility issues encountered with silica-based FBGs. Polymer FBGs exhibit improved mechanical robustness, making them suitable for the harsh conditions within SRMs [45]. With the provided strain sensitivity being much better than that of glass/silica optical FBGs (GOFBGs) [46], the strains that can be measured exceed 6% [47] or even 10%.
The main drawback of typical POF FBG sensors is the interrogation process. Indeed, POFs usually operate in a multimode regime, meaning they support multiple propagation modes for light within the fiber core. Interrogating FBGs in multimode fibers, including POFs, is more complex compared with single-mode fibers (SMFs) due to the overlapping spectra from different modes [48]. Among the most common techniques used to overcome this limitation involves mode demultiplexing or the use of mode-division multiplexers (MDMs) [49]. Mode-demultiplexing involves employing specialized devices or algorithms to distinguish the responses from different modes. For instance, modal filtering can be employed to selectively couple light into specific modes of the multimode fiber, making it possible to isolate the reflection from the desired mode. MDMs can selectively couple light into specific modes and decouple it after the transmission through the fiber. By employing MDMs, it is possible to separate the modes, allowing for individual interrogation of the FBGs inscribed in different modes. Additionally, advanced interrogation systems using algorithms and signal-processing techniques have been developed to analyze the complex responses of multimode FBGs. These systems utilize mathematical methods to distinguish the different modes’ signals and interpret the data accurately. However, these approaches are very complex with very high interrogation costs, and not suitable for demanding applications such as SRM or aerospace applications where proven and robust solutions are needed.
Recently, novel approaches have emerged for developing single-mode FBGs in few-mode polymer optical fibers (FM-POF) FBGs [50][51][52][53] by using special laser-based inscription techniques. Implementing a single FBG in multi-/few-mode polymer optical fibers [54] enables the integration of the favorable characteristics of POFs (higher elasticity) with the capability for interrogation by standard FBG interrogation units typically used for glass-based FBGs.
FBGs in single-mode fibers (SMFs) have been implemented also in microstructured polymer optical fibers (photonic crystal fibers, or PCFs); however, this is a more complex process both for the Bragg Grating inscription process and for the termination and interconnection of these PCFs to standard silica-based telecom SMFs, resulting in serious handling difficulty. The primary technical limitation that hindered the use of FBGs in single-mode POFs is the difficulty of consistently and reliably producing truly single-mode fibers with a solid core and minimal dimensions, as the fiber drawing process, in this case, is exceptionally demanding and poses significant challenges. Therefore, there are no widely commercially available single-mode, single-core POFs yet. However, there is increasing research activity on and limited production of experimental single-mode POFs [44] featuring directly defined FBGs. Robust and customizable solutions of POF FBGs are anticipated to emerge in the near future.

4.4. Distributed Fiber Optic Sensors

Fiber-optic sensors can be classified as point or distributed. FBG-based sensors are essentially multipoint sensors with a potentially indirect distributed capability depending on the number of embedded BGs in the fiber. Distributed sensors can monitor several thousand points simultaneously, thus providing a drastically reduced cost per sensed point. However, depending on their specific technology and performance requirements, their total cost can be particularly high. The operational principles of distributed fiber-optic sensors can be based on Rayleigh, Raman, or Brillouin scattering effects. Rayleigh scattering is an elastic process, attributed to inhomogeneity in the density of the optical material. Brillouin and Raman scattering-based sensors’ operation is based on propagating light interacting with the propagating acoustic phonons and molecular vibrations of the optical fiber, respectively, exhibiting a frequency shift with respect to the incoming propagating light in the fiber. The best-suited distributed technologies for real-time SHM are considered to be those based on Rayleigh and Brillouin scattering, while Raman-based sensors are commercially available for temperature monitoring. Brillouin sensors are relatively costly; however, they are accurate and offer high spatial resolution and extended sensing range. On the other hand, Rayleigh distributed sensors are relatively fast and very sensitive, while their interrogation costs depend strongly on the target resolution performance [23].
Such distributed sensors are better suited for long-scale systems; for limited-scale SRM systems, employment is considered cost inefficient due to the very high costs of interrogation units. Furthermore, FBGs provide increased flexibility, as they can be customized for measuring a number of mechanical parameters or chemical and environmental factors, and all of these different sensors can be interrogated by a single unit.

5. Machine Learning as an Enabling Tool for the CBM of SRMs

The integration of cutting-edge technologies such as computational intelligence, deep learning algorithms, machine learning, and neural networks has revolutionized the way researchers approach defect diagnosis and predictive maintenance strategies [55][56][57]. One of the primary applications of machine learning in this domain involves the accurate interpretation of continuously collected data from sensors embedded within SRMs [58]; machine learning algorithms can identify patterns and anomalies associated with strain, temperature, and other critical factors. Nondestructive imaging techniques have also been used in this field of defect diagnosis [59][60][61]. These algorithms learn to recognize precursor signals that indicate potential issues, allowing engineers to proactively address problems before they escalate. Machine learning models, trained on historical data from FBGs or other sensors, can identify specific patterns associated with different types of faults or structural degradation in SRMs. Whether detecting microcracks, delamination, or other forms of damage, these algorithms can provide detailed insights, aiding engineers in understanding the nature and severity of these issues.
Discriminating normal operational variation from abnormal behavior is feasible through neural network and machine learning approaches. At the same time, they make it possible to detect subtle changes that could go unnoticed through traditional analysis methods. Scientific approaches published in the field of SHM depict the necessity to study uncertainties as a crucial aspect affecting the interpretation of sensor data in the route to diagnosing the structural integrity of a material; however, only a restricted number of studies explicitly refer to SRM models [62][63].
Moreover, various sophisticated algorithms can optimize the placement of state of the art sensing elements, such as DBSTs or FBGs [64], within SRMs. By analyzing computational models and historical data, these algorithms [65][66][67][68] can suggest the most strategic locations for sensors to maximize their effectiveness. This ensures that the acquired data are not only comprehensive but also highly relevant, enhancing the overall efficiency of the SHM system [69][70].


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