Comparative Analysis of Low-Cost and Commercial Sensors in Structural Monitoring Under Seismic Simulations

Final Thesis developed by: Martin GRANIER Directed by: Seyedmilad KOMARIZADEHASL Jose TURMO CODERQUE Master in: Structural and Construction Engineering Barcelona, January 2025 Department of Civil and Environmental Engineering MASTER FINAL THESIS Comparative Analysis of Low-Cost and Commercial Sensors in Structural Monitoring Under Seismic Simulations Martin GRANIER 2 Comparative Analysis of Low-Cost and Commercial Sensors in Structural Monitoring Under Seismic Simulations Abstract: Structural Health Monitoring (SHM) plays a critical role in ensuring the safety and longevity of buildings, especially in earthquake-prone regions. Traditional SHM systems often rely on high-cost commercial sensors, which can limit widespread adoption due to financial constraints. This study conducts a comparative analysis of low-cost and commercial sensors to evaluate their efficacy in structural monitoring under seismic simulation conditions. The primary objectives are to assess the accuracy, reliability, and cost-effectiveness of low-cost sensors relative to their commercial counterparts and to determine their suitability for large-scale SHM applications during seismic events. An experimental setup was established using a scaled structural model subjected to various seismic simulations mimicking different earthquake intensities. Both low-cost sensors and commercial sensors were strategically installed on the model to capture dynamic responses. Data collection involved continuous monitoring over multiple simulation trials, followed by rigorous statistical analysis. The results indicate that low-cost sensors demonstrate comparable performance to commercial sensors in capturing essential structural responses, particularly in moderate seismic conditions. While some discrepancies were noted in high-intensity simulations, the low-cost sensors maintained acceptable accuracy levels for practical SHM purposes. Additionally, a significant reduction in overall system costs was achieved without substantial sacrifices in data quality. The study highlights the potential of integrating lowcost sensors into SHM frameworks, promoting more accessible and sustainable monitoring solutions for diverse infrastructural applications. In conclusion, this research supports the viability of low-cost sensors as effective alternatives to commercial sensors in structural monitoring under seismic conditions. The findings advocate for their adoption in resource-constrained environments, fostering enhanced structural safety through affordable and reliable monitoring technologies. Future work will explore long-term deployment scenarios and the integration of advanced data analytics to further optimize SHM systems. Keywords: Structural Health Monitoring, Low-Cost Sensors, Commercial Sensors, Seismic Simulation, Sensor Accuracy, Cost-Effectiveness Martin GRANIER 3 Résumé: Le contrôle de santé des structures (CSS) joue un rôle crucial pour assurer la sécurité et la longévité des bâtiments, en particulier dans les régions sujettes aux tremblements de terre. Les systèmes traditionnels de suivi de santé structurelle reposent souvent sur des capteurs commerciaux coûteux, ce qui peut limiter leur adoption généralisée en raison de contraintes financières. Cette étude réalise une analyse comparative entre des capteurs à faible coût et des capteurs commerciaux afin d’évaluer leur efficacité dans la surveillance structurelle sous des conditions de simulation sismique. Les objectifs principaux sont d’évaluer la précision, la fiabilité et le rapport coût-efficacité des capteurs à faible coût par rapport à leurs homologues commerciaux et de déterminer leur adéquation pour des applications de CSS à grande échelle lors d’événements sismiques. Un dispositif expérimental complet a été établi en utilisant un modèle structurel à moindre échelle soumis à diverses simulations sismiques mimant différentes intensités de séismes. Des capteurs à faible coût ainsi que des capteurs de qualité commerciale ont été installés stratégiquement sur le modèle pour capturer les réponses dynamiques. La collecte des données a impliqué une surveillance continue au cours de plusieurs essais de simulation, suivie d’une analyse statistique rigoureuse. Les résultats indiquent que les capteurs à faible coût démontrent des performances comparables à celles des capteurs commerciaux pour capturer les réponses structurelles essentielles, en particulier dans des conditions sismiques modérées. Bien que certaines divergences aient été notées lors de simulations à haute intensité, les capteurs à faible coût ont maintenu des niveaux de précision acceptables pour des applications pratiques de SHS. De plus, une réduction significative des coûts globaux du système de contrôle a été réalisée, sans sacrifices substantiels de la qualité des données. L’étude met en lumière le potentiel d’intégration des capteurs à faible coût dans les cadres de CSS, favorisant des solutions de surveillance plus accessibles et évolutives pour diverses applications infrastructurelles. En conclusion, cette recherche soutient la viabilité des capteurs à faible coût en tant qu’alternatives efficaces aux capteurs commerciaux dans le contrôle de santé des structures sous conditions sismiques. Les résultats préconisent leur adoption dans des environnements aux ressources limitées, favorisant une sécurité structurelle accrue grâce à des technologies de surveillance abordables et fiables. Les travaux futurs exploreront des scénarios de déploiement à long terme et l’intégration d’analyses de données avancées pour optimiser davantage les systèmes de CSS. Mots-clés: Surveillance de la santé structurelle, Capteurs à faible coût, Capteurs commerciaux, Simulation sismique, Précision des capteurs, Rapport coût-efficacité Martin GRANIER 4 Acknowledgements I would first like to thank the two engineering schools that enabled me to pursue this dual degree, provided me with excellent training, and prepared me for the professional world in the best possible way: the École Spéciale des Travaux Publics (ESTP) and the Universitat Politècnica de Catalunya (UPC). Additionally, I would like to express my gratitude to my two TFM supervisors, José Turmo and Seyedmilad Komarizadehasl, for their invaluable knowledge and unwavering support. Furthermore, I want to thank the entire professional team at COPCISA, who allowed me to carry out my TFM alongside my internship as an assistant construction manager. A special thanks to Pedro Castellanos, Marina Gonzalez, and Carlos Garrote. Lastly, I would like to thank all the members of my family, who have always supported and believed in me, even while I was abroad in an environment outside of my comfort zone. Martin GRANIER 5 Table of Contents List of Figures and Tables ................................................................................................ 7 Chapter 1: Introduction ..................................................................................................... 9 1.1 Background ....................................................................................................... 9 1.2 Problem Statement .......................................................................................... 10 1.3 Research Objectives & Questions .................................................................. 10 1.4 Scope & Significance of the Study ................................................................. 11 1.5 Thesis Organization ........................................................................................ 12 Chapter 2: Literature Review ......................................................................................... 13 2.1 Structural Monitoring System ........................................................................ 13 2.1.1 Designing a SHM system ....................................................................... 13 2.2 Types of Sensors Used in SHM ...................................................................... 15 2.3 Low-Cost Sensors ........................................................................................... 16 2.4 Commercial Sensors ....................................................................................... 17 2.5 Seismic Simulations in SHM .......................................................................... 17 2.6 Summary ......................................................................................................... 18 Chapter 3: Sensor Specifications and Comparative Framework .................................... 19 3.1 Low-Cost Sensor ............................................................................................ 19 3.2 Commercial Sensor ........................................................................................ 20 3.3 Comparative Framework ................................................................................ 20 Chapter 4: Methodology ................................................................................................. 22 4.1 Experimental Setup ........................................................................................ 22 4.2 Theory ............................................................................................................. 23 4.2.1 Structural Dynamics ............................................................................... 25 4.2.2 Frequency Domain Decomposition and Peak Picking method .............. 28 4.3 Research Design ............................................................................................. 30 4.4 Selection of Sensors ....................................................................................... 30 4.5 Seismic Simulation Procedures ...................................................................... 30 4.6 Data Collection Methods & Analysis Techniques ......................................... 31 4.6.1 Absolute Relative Error ................................................................................. 32 4.6.2 Modal Assurance Criterion ............................................................................ 32 Chapter 5: Experimental Results .................................................................................... 33 5.1 Data Presentation ............................................................................................ 33 5.1.1 Earthquake 1 .................................................................................................. 33 5.1.2 Earthquake 2 .................................................................................................. 35 5.1.3 Sine 1 ............................................................................................................. 37 5.1.4 Sine 2 ............................................................................................................. 38 Martin GRANIER 6 5.1.5 Sine 3 ............................................................................................................. 40 5.1.6 Impact ............................................................................................................ 42 5.2 Comparative Analysis .................................................................................... 44 Chapter 6: Discussion ..................................................................................................... 45 6.1 Interpretation of Findings ............................................................................... 45 6.2 Implications for Structural Health Monitoring ............................................... 45 6.3 Limitations of the Study ................................................................................. 45 Chapter 7: Sustainability analysis and ethical implications ........................................... 46 Chapter 8: Conclusion .................................................................................................... 47 8.1 Summary of Research ..................................................................................... 47 8.2 Conclusions .................................................................................................... 47 8.3 Future Work .................................................................................................... 47 References ...................................................................................................................... 48 Appendices ..................................................................................................................... 51 Martin GRANIER 7 List of Figures and Tables Figure 1: Conceptual diagram of the utilization of SHM ................................................. 9 Figure 2: Conceptual diagram of a data acquisition system ........................................... 14 Figure 3: Conceptual diagram of data flow in acquisition systems ................................ 15 Figure 4: Picture of the LARA sensing part and it acquisition part ............................... 19 Figure 5: Picture of the PCB 3713B112G sensor without and with connection cable ... 20 Figure 6: Picture of the experimental setup taken the 08/07/2027 ................................. 22 Figure 7: Picture of the design drawing in AutoCAD translated from Chinese ............. 23 Figure 8: Deformation scheme of the structure .............................................................. 24 Figure 9: First four mode shapes of a simply supported beam ....................................... 27 Figure 10: First four natural frequencies for the Peak Picking method.......................... 29 Figure 11: Line time of the events which will occur to test the structure ...................... 31 Figure 12: General overview of the LARA’s response .................................................. 33 Figure 13: LARA’s response against Earthquake 1 excitation....................................... 34 Figure 14: Commercial peaks of frequencies selected for “Earthquake1” ..................... 34 Figure 15: LARA’s peaks of frequencies selected for “Earthquake1” ........................... 34 Figure 16: LARA’s response against “Earthquake2” excitation .................................... 35 Figure 17: Commercial peaks of frequencies selected for “Earthquake2” excitation .... 36 Figure 18: LARA’s peaks of frequencies selected for “Earthquake2” excitation .......... 36 Figure 19: LARA’s response against “Sine1” excitation .............................................. 37 Figure 20: Commercial peaks of frequencies selected for “Sine1” excitation ............... 37 Figure 21: LARA’s peaks of frequencies selected for “Sine1” excitation ..................... 38 Figure 22: LARA’s response against “Sine2” excitation .............................................. 39 Figure 23: Commercial peaks of frequencies selected for “Sine2” excitation .............. 39 Figure 24: LARA’s peaks of frequencies selected for “Sine2” excitation .................... 39 Figure 25: LARA’s response against “Sine3” excitation .............................................. 40 Figure 26: Commercial peaks of frequencies selected for “Sine3” excitation .............. 41 Figure 27: LARA’s peaks of frequencies selected for “Sine3” excitation .................... 41 Figure 28: LARA’s response against “Impact” excitation ............................................. 42 Figure 29: Commercial peaks of frequencies selected for “Impact” excitation ............. 42 Figure 30: LARA’s peaks of frequencies selected for “Impact” excitation ................... 43 Figure 31: Pictures from the experimental setup, focus on the column connection ....... 46 Martin GRANIER 8 Table 1: Summary of key aspects in current SHM ......................................................... 10 Table 2: Summary of triaxial MEMS sensors already existing [10] .............................. 12 Table 3: Selection criteria for choosing sensors [15] ..................................................... 14 Table 4: Comparative table of the characteristics of the sensors ................................... 21 Table 5: 4 first eigenfrequencies of the sensors during “Earthquake1” ......................... 35 Table 6: 4 first mode shapes of the sensors during “Earthquake1” ................................ 35 Table 7: 4 first eigenfrequencies of the sensors during “Earthquake2” ......................... 36 Table 8: 4 first mode shapes of the sensors during “Earthquake2” ................................ 37 Table 9: 4 first eigenfrequencies of the sensors during “Sine1” .................................... 38 Table 10: 4 first mode shapes of the sensors during “Sine1” ......................................... 38 Table 11: 4 first eigenfrequencies of the sensors during “Sine2” .................................. 40 Table 12: 4 first mode shapes of the sensors during “Sine2” ......................................... 40 Table 13: 4 first eigenfrequencies of the sensors during “Sine3” .................................. 41 Table 14: 4 first mode shapes of the sensors during “Sine3” ......................................... 42 Table 15: 4 first eigenfrequencies of the sensors during “Impact” ................................ 43 Table 16: 4 first mode shapes of the sensors during “Impact” ....................................... 43 Martin GRANIER 9 Chapter 1: Introduction After the development of construction industry in the past century, many structures such as bridges, high-rise buildings and other types of more common buildings such as housings were put up and are now daily used by human being. Indeed, the buildings, which are made to accommodate human activity, need to satisfy a series of functions intended to assure safety, protection and the conditioning needed to realize any kind of activities in its. 1.1 Background The structural system of those buildings has three important functions. It has to be vertically and horizontally stable, it also has to be resistant against gravity, horizontal actions like and climate and rheological actions and finally, it has to be rigid enough against vertical and horizontal actions [1]. Today’s existing structures are generally designed for a service life in between 50 to 120 years, depending on the country and the built asset. However, they are inevitably exposed to the natural environment in which they were built, it means that potential external horizontal actions such as wind or seismic actions can put in danger the structure. As it is generally done in the characterization of wind action by measuring the real pressure gradient acting on a realistic structure simulation in wind tunnels, it is also Figure 1: Conceptual diagram of the utilization of SHM Martin GRANIER 16 Accelerometers are essential for detecting vibrations and dynamic responses of structures. They measure the rate of change in velocity which allows to convey the motion of the structures under dynamic loads, such as wind, earthquakes or even traffic loads. For example, the deployment of accelerometers on the Golden Gate Bridge helps monitor vibrations caused by wind and traffic [16]. Strain gauges are employed to measure the strain in structural components. These sensors help detect stress distribution and deformation, providing insights into potential weaknesses and fatigue in materials. For instance, strain gauges were used in the monitoring of the Millau Viaduct in France to assess the bridge’s load-bearing capacity [17]. Displacement sensors, including inclinometers, are used to measure the displacement and angular tilt of structures. Inclinometers are particularly effective in monitoring landslides, dam movement and the tilt of tall buildings. A relevant example is the use of inclinometers to monitor the Leaning Tower of Pisa’s tilt correction efforts [18]. The use of these sensors in SHM enables the continuous monitoring of structural responses, early detection of penitential failures, and the implementation of timely maintenance strategies, thereby enhancing safety and prolonging the lifespan of infrastructure. 2.3 Low-Cost Sensors Recent advancements in sensor technology have led to the development of low-cost sensors for SHM applications. These sensors offer an economical alternative for widespread monitoring without compromising essential performance characteristics. Examples of low-cost sensors include Micro-Electro-Mechanical Systems (MEMS) accelerometers, fiber optic sensors, and piezoelectric sensors. MEMS accelerometers, such as ADXL345, provide cost-effective vibration for monitoring solutions suitable for widespread deployment across infrastructure networks [19]. Fiber optic sensors, like Fiber Bragg Grating (FBG) sensors, have seen cost reduction through mass production and improved manufacturing processes [20]. Piezoelectric sensors, known for their simplicity and cost-effectiveness, are used to detect vibrations and pressure changes in structural components, exemplified by the use of PZT sensors in bridge monitoring [21]. Additionally, the Low-cost Adaptable Reliable Accelerometer (LARA) sensor, offers an innovative and affordable solution for real-time structural monitoring. LARA sensors are designed to deliver accurate vibration data with minimal energy consumption, making them suitable for large-scale deployments in infrastructure networks. A notable example of their application is in the monitoring of Tehran’s Milad Tower, where LARA sensors are utilized to detect structural vibrations and potential stress points [22]. Martin GRANIER 17 Technological advancements in wireless communication, data processing and energy harvesting have further enhanced the capabilities of low-cost sensors. These improvements allow for more extensive and real-time data collection, leading to more informed decision-making in SHM. In addition to, the integration of Internet of Things (IoT) technologies facilitates remote monitoring and data analytics by reducing the need for manual inspections and lowering operational costs [23]. 2.4 Commercial Sensors On another hand, commercial-grade sensors are designed for high-performance SHM applications where accuracy, durability and reliability are paramount. These sensors include high-precision accelerometers, laser displacement sensors and advanced fiber optic sensors. High-end accelerometers used in commercial SHM systems, such as the PCB Piezotronics accelerometer MEMS series, provide superior sensitivity and stability, enabling accurate detection of even the slightest structural movements [24]. They have a price of around $500 [25]. Laser displacement sensors, like the Keyence LK-G series, offer non-contact measurement capabilities with exceptional precision, making them ideal for monitoring critical infrastructure such as bridges and high-rise buildings [26]. Advanced fiber optic sensors, such as those developed by Luna Innovations, are prized for their immunity to electromagnetic interference and ability to operate in harsh environments, ensuring consistent performance over extended periods [27]. Usually, the feature of commercial sensors include rugged designs, high data resolution and advanced signal processing capabilities. Their reliability is critical for applications where data accuracy can influence safety-critical decisions. In a same way, the cost of these sensors in in general much higher due to their specialized materials, sophisticated designs and rigorous testing standards. Cost considerations involve not only the initial purchase price but also installation, calibration and maintenance expenses. For now and despite higher costs, the long-term benefits of deploying commercial-grade sensors in critical infrastructure monitoring explains the justification of the investment through enhanced safety, reduced downtime and prolonged service life of structures. 2.5 Seismic Simulations in SHM Seismic simulations play a crucial role in testing and validating Structural Health Monitoring (SHM) systems. By replicating the dynamic effects of seismic events, these simulations enable engineers to evaluate how structures and their monitoring systems respond to earthquake-induced stresses. This proactive approach helps identify vulnerabilities and improves the reliability of SHM systems under real-world seismic conditions. Martin GRANIER 18 Common methodologies for seismic simulations include numerical modeling and physical shake table testing. Numerical modeling utilizes finite element analysis software, such as GiD or SAP2000, to simulate how structures react to various seismic loads. These models help predict structural behavior, optimize sensor placement and evaluate system performance under different earthquake scenarios. Shake table testing involves placing scaled structural models on a movable platform that simulates ground motions. Facilities like UC San Diego Large High-Performance Outdoor Shake Table (LHPOST) and the Universitat Politècnica de Catalunya (UPC) in Barcelona have been pivotal in conducting seismic tests on structural models [28]. Additionally, tools such as OpenSees (Open System for Earthquake Engineering Simulation) provide open-source platforms for seismic analysis, enabling detailed simulations of structural responses. Hybrid simulation techniques that combine physical testing with numerical models further enhance the accuracy and efficiency of seismic assessments. Seismic simulations are indispensable for validating SHM systems, optimizing sensor networks, and developing more resilient infrastructure. They enable engineers to design safer structures, reduce earthquake-related risks, and ensure that SHM systems remain effective during and after seismic events. 2.6 Summary This chapter reviews the key themes surrounding SHM, including its systems, sensor types, cost considerations, and seismic simulations. Structural Health Monitoring involves strategies to detect and characterize damage in structures such as bridges, buildings, and aircraft, enhancing safety, preventing failures, and optimizing maintenance schedules. Effective SHM design requires characterizing the structure, identifying measurable phenomena, selecting suitable sensors, and using robust data acquisition systems. Statistical methods play a vital role in diagnosing structural health issues. Common SHM sensors include accelerometers for detecting vibrations, strain gauges for measuring stress, and displacement sensors like inclinometers for monitoring structural tilt and deformation. Recent advancements in sensor technology have led to cost-effective solutions such as low-cost MEMS accelerometers enabling widespread SHM deployment. On the other hand, high-end commercial sensors, including laser displacement and advanced fiber optic sensors, offer superior precision and durability for critical infrastructure, justifying their higher costs. Seismic simulations, including numerical modeling and shake table testing, replicate earthquake impacts to validate SHM systems. Tools like numerical analysis software optimize sensor researches and by the same way, improve structural resilience against seismic events. These technologies and methods collectively contribute to safer, more reliable, and cost-effective structural monitoring systems. Martin GRANIER 19 Chapter 3: Sensor Specifications and Comparative Framework In this chapter, two sensors will be analyzed more in details. First the LARA one will be chosen to play the role of the low-cost sensor. However, as the commercial sensor used for this thesis experiment is common and unknown, a very famous commercial one will be used to play the role of the commercial sensor, namely the PCB 3713B112G. 3.1 Low-Cost Sensor The Low-cost Adaptable Reliable Accelerometer (LARA) is a specialized solution designed by UPC researchers to address the financial constraints associated with traditional Structural Health Monitoring systems. SHM is vital for ensuring the safety and durability of civil infrastructure by detecting and characterizing damage in its early stages, thus preventing costly repairs and ensuring operational safety. Concerning the hardware part, LARA is a low-cost triaxial accelerometer developed using Arduino technology, optimized for SHM applications. It hardware consists of several components. The MEMS Accelerometer Sensor in LARA provides precise acceleration measurements in three axes. The Arduino Microcontroller acts as the core processing unit responsible for data acquisition, signal processing, and communication, managing data collection and synchronization. Multiplexers and cables are utilized for connecting multiple sensors and ensuring reliable data transmission. The system is powered by a battery-powered supply designed for field deployment, ensuring continuous operation. Protective enclosures safeguard internal electronics from environmental factors. Concerning the LARA software architecture, LARA’s framework integrates various components for efficient data acquisition and processing. The data acquisition module captures acceleration data from the MEMS sensor at a sampling rate of 345 Hz, optimized for structural monitoring. A synchronization algorithm ensures precise time alignment of data from multiple sensors using a timestamp mechanism with microsecond resolution. Noise filtering and signal processing algorithms improve data quality, addressing issues like high noise density. The data resampling module adjusts data sampling rates for compatibility with frequency domain analysis methods. A data transmission protocol facilitates data transfer from the accelerometer to storage or analysis systems, leveraging Internet of Things (IoT) technology for remote monitoring. Figure 4: Picture of the LARA sensing part and it acquisition part Sensing Part Acquisition Part Martin GRANIER 20 3.2 Commercial Sensor On the other hand, The PCB 3713B112G is a high-end triaxial MEMS accelerometer designed for precision structural monitoring applications. It hardware features include advanced MEMS sensing elements that deliver ultra-low noise density and high sensitivity. The accelerometer is integrated with high-performance signal conditioning electronics to ensure accurate data acquisition. It operates with a wide dynamic range and is enclosed in a robust, environmentally sealed casing for durability in harsh conditions. The device supports high-speed data transmission via industrial-grade connectors and power supply stability for continuous long-term monitoring. Moreover, the PCB 3713B112G employs sophisticated embedded software for real-time data acquisition and processing. It includes advanced filtering algorithms to eliminate noise and signal distortions, providing high-fidelity data. The sensor integrates seamlessly with data acquisition systems through industry-standard protocols. Its software supports customizable data sampling rates and automatic calibration routines to maintain precision. Additionally, the sensor offers remote monitoring and diagnostics through secure communication interfaces, ensuring reliability in critical monitoring scenarios. 3.3 Comparative Framework To get an idea of the price difference between these two sensors, it is important to compare their frameworks in order to find plausible explanations for this cost gap of around 2000€. Hereinafter a table resuming the principal characteristics of the two compared sensors. Both of them offer a robust protection and have the same measurement range but it is important to notice that there are some discrepancies which can explain a part of the price gap. Indeed, the LARA’s noise density is more than twice as much as the commercial one, indicating lower performance in environments where low noise is critical. Moreover, the interval of frequency response of the commercial sensor is four times wider than the LARA one, making it more suitable for applications requiring detection of higher frequency vibrations. Meanwhile the commercial sensor offers higher resolution and higher sensitivity, making it better for small dynamic charges, the LARA sensor has a higher sampling rate, enabling it to capture more data points in a given time. Figure 5: Picture of the PCB 3713B112G sensor without and with connection cable Martin GRANIER 21 Item PCB 3713B112G LARA Type or Model MEMS accelerometer MEMS accelerometer Dimension 20,3 x 20,3 x 20,3mm 40 x 40 x 5mm Measurement Range as accelerometer ± 2.0 g ± 2.0 g Noise density as accelerometer 22,9µg/√Hz 51µg/√Hz Resolution as accelerometer 250µg 31µg Frequency Response as accelerometer 0 – 250Hz 0 – 61Hz Sampling Rate as accelerometer 200 Hz 345 Hz Sensitivity as accelerometer 1000 mV/g 625 mV/g Operating temperature -54oC to +121oC -40oC to +85oC Communication Integral cable Ethernet or USB Power Source Integral cable Ethernet or USB Power Consumption ≤ 6mA 200mA @ 5V Waterproof Hermetic sealing IP67 compliant Data collection Integral cable Wireless Table 4: Comparative table of the characteristics of the sensors Martin GRANIER 22 Chapter 4: Methodology In this chapter, we will discuss the methodology used to successfully conduct the experimental study aimed at comparing commercial and low-cost sensors. To do so, the experimental setup will de detailed along with all the theory required to perform the data analysis. 4.1 Experimental Setup The experiment took place during summer 2024 in China. This involves setting up a threestory miniature building structure at a scale of approximately 1:10, equipped with a lowcost sensor and a commercial one on each floor, as shown in the picture taken during the execution of this experiment below. Additionally, the structure was placed on a shaking table to subject it to earthquake-like movements [29]. The shaking table will excite the structure in a unique direction, namely the Y-direction in this case. Figure 6: Picture of the experimental setup taken the 08/07/2027 LARA 1 + Commercial LARA 2 + Commercial LARA 3 + Commercial LARA 4 + Commercial Martin GRANIER 23 As it can be easily seen, there are four stories of sensors. Then, there will be eight sources of data collection which will have to be well organized to easier compute them for the analysis. To do so, the low-cost sensors will have a number from 1 to 4, 1 corresponding to the top one, and four to the bottom one. Now, to talk about the layout of the structure, it is important to refer to the design drawing file the Chinese engineers realized. It is a basic layout of a three-story building with four corner columns made of an aluminum alloy and with the following characteristics: 755𝑚𝑚 𝑙𝑜𝑛𝑔 / 50𝑚𝑚 𝑤𝑖𝑑𝑒 / 2𝑚𝑚 𝑡ℎ𝑖𝑐𝑘 As the spacing of the stories is about 240mm, if the scale is about 1:10, it would mean that the real building represented should be a three-story building of 7,55m height, with three stories of about 2,50m height as it is illustrated in the following picture: 4.2 Theory In this part, it will be explained all the theoretical knowledge which is required to realize the data analysis of the low-cost and commercial sensors. As the structure is already well defined, it is now the time to go further and to define the characteristics of each elements of the structure with the following scheme: Figure 7: Picture of the design drawing in AutoCAD translated from Chinese Martin GRANIER 24 By using the Newton’s laws applied to the solid, here the three slabs: ∑𝐹𝑒𝑥𝑡=𝑚𝑎󰇘 (1) It is now possible to deduce that the system to solve from the three story building is: 𝑚1𝑢󰇘1(𝑡)=−𝑘1𝑢1(𝑡)−𝑐1𝑢󰇗1(𝑡)+𝑘2(𝑢2(𝑡)−𝑢1(𝑡))+𝑐2(𝑢󰇗2(𝑡)−𝑢󰇗1(𝑡)) (2) 𝑚2𝑢󰇘2(𝑡)=𝑘2(𝑢2(𝑡)−𝑢1(𝑡))+𝑐2(𝑢󰇗2(𝑡)−𝑢󰇗1(𝑡))−𝑘3(𝑢3(𝑡)−𝑢2(𝑡))−𝑐3(𝑢󰇗3(𝑡)−𝑢󰇗2(𝑡)) (3) 𝑚3𝑢󰇘3(𝑡)=𝑘3(𝑢3(𝑡)−𝑢2(𝑡))+𝑐3(𝑢󰇗3(𝑡)−𝑢󰇗2(𝑡))+𝑝3(𝑡) (4) As the structure is free to move and so the top slab is also free, it can be assumed that 𝑝3(𝑡)=0. The equation (4) becomes: 𝑚3𝑢󰇘3(𝑡)=𝑘3(𝑢3(𝑡)−𝑢2(𝑡))+𝑐3(𝑢󰇗3(𝑡)−𝑢󰇗2(𝑡)) (5) To facilitate the solving of the three equations system constituted of equations (2), (3) and (5), a matrix form is presented as below: Figure 8: Deformation scheme of the structure Martin GRANIER 25 𝑀𝑈󰇘(𝑡)+𝐶𝑈󰇗(𝑡)+𝐾𝑈(𝑡)=0 (6) With the following defined matrixes: 𝑀=(𝑚10 0 0 𝑚20 0 0 𝑚3) 𝐶=(𝑐1+𝑐2−𝑐20 −𝑐2𝑐2+𝑐3−𝑐3 0 −𝑐3𝑐3) 𝐾=(𝑘1+𝑘2−𝑘20 −𝑘2𝑘2+𝑘3−𝑘3 0 −𝑘3𝑘3) And the displacement function with its time derivatives: 𝑈(𝑡)=(𝑢1(𝑡) 𝑢2(𝑡) 𝑢3(𝑡)) 𝑈󰇗(𝑡)=(𝑢󰇗1(𝑡) 𝑢󰇗2(𝑡) 𝑢󰇗3(𝑡)) 𝑈󰇘(𝑡)=(𝑢󰇘1(𝑡) 𝑢󰇘2(𝑡) 𝑢󰇘3(𝑡)) Now, the problem resides in solving the equation (6) which has a form of an homogeneous system and, to do so, it is important to look back on structural dynamics. 4.2.1 Structural Dynamics Structural dynamics is a comprehensive study of structures behavior not only under external excitations but also in the absence of external forces where dynamic characteristics of the structure influence it behavior, including free vibrations. As the study is based on a single degree of freedom, namely the Y direction (see Figure 5), the Single Degree of Freedom (SDOF) model will be used to solve equation (6). It assumes that the structure can be represented as a mass 𝑚 attached to a spring 𝑘 and a damping system 𝑐. The equation of motion for an SDOF system is as follows: 𝑚𝑥󰇘(𝑡)+𝑐𝑥󰇗(𝑡)+𝑘𝑥(𝑡)=0 (7) If we consider the undamped case, ignoring damping, the equation (6) is reduced to: 𝑚𝑥󰇘(𝑡)+𝑘𝑥(𝑡)=0 (8) Assuming that the system undergoes harmonic motion in free vibration because no external forces are acting, equation (8) can be written as: Martin GRANIER 32 After that, Operational Modal Analysis (OMA) is performed using the Frequency Domain Decomposition (FDD) method to analyze the structural behavior. MATLAB's freely available FDD code is employed [32] to derive critical dynamic characteristics from the acceleration data recorded during the monitoring of civil engineering structures exposed to environmental noise. This analysis computes the mode shapes, the eigenfrequencies and the modal damping ratios. Then, to correlate the accuracy of the two different types of sensors, a comparative study will be carried out between its eigenfrequencies and its mode shapes. To do so, it requires new mathematical tools such as the Modal Assurance Criterion (MAC), which is a statistical indicator used to quantify the correlation between two mode shapes, also called eigenvectors. On the other hand, the Absolute Relative Error (ARE) will help quantifying the accuracy of the measured eigenfrequencies of both sensors. 4.6.1 Absolute Relative Error In order to compare the accuracy of the measured eigenfrequencies of the two sensors, the absolute relative error formula will be used. 𝐴𝑅𝐸%=|𝑓𝑖,𝐿𝐴𝑅𝐴−𝑓𝑖,𝑐𝑜𝑚𝑚𝑒𝑟𝑐𝑖𝑎𝑙 𝑓𝑖,𝑐𝑜𝑚𝑚𝑒𝑟𝑐𝑖𝑎𝑙 |×100 (17) Where, - 𝑓𝑖,𝐿𝐴𝑅𝐴 represents the 𝑖𝑡ℎ eigenfrequency of the LARA sensor - 𝑓𝑖𝑐𝑜𝑚𝑚𝑒𝑟𝑐𝑖𝑎𝑙 represents the 𝑖𝑡ℎ eigenfrequency of the commercial sensor 4.6.2 Modal Assurance Criterion To compare the mode shapes of the two sensors under study, it is essential to compute the MAC. To calculate the MAC of two 4x4 matrixes, these ones should be compared in a way that generalizes the vector formula, namely: 𝑀𝐴𝐶(𝐶,𝐿)=|𝑣𝑒𝑐(𝐶)𝑇𝑣𝑒𝑐(𝐿)|² (𝑣𝑒𝑐(𝐶)𝑇𝑣𝑒𝑐(𝐶)).(𝑣𝑒𝑐(𝐿)𝑇𝑣𝑒𝑐(𝐿)) (18) Where, - 𝐶 refers to the commercial sensor mode shape matrix - 𝐿 refers to the commercial sensor mode shape matrix - 𝑣𝑒𝑐(Φ) stacks the columns of Φ in a 16x1 vector - 𝑣𝑒𝑐(Φ)𝑇 is the transpose matrix of Φ with a size 1x16 To calculate it in an easier way, a MATLAB code will be used, namely “compute_MAC” (see the code in Appendix). Martin GRANIER 33 Chapter 5: Experimental Results In this chapter, all the experimental results will be presented and ordered following the line time of the excitations the sensors were subjected to. 5.1 Data Presentation At first, it is important to present a general overview of the response of the LARA sensor. To do so, it will be selected the total time of the experiment, that is to say from 9:42:00 (UTC+7) to 10:01:00 (UTC+7). Unfortunately, the data of the commercial sensor was only collected during the excitations periods. Therefore, there is no commercial data during the free movement period of the structure under study. 5.1.1 Earthquake 1 To start comparing the two sensors, it will be first analyzed the seismic simulation “Earthquake 1” from 9:42:02 (UTC+7) to 9:42:15 (UTC+7). Figure 12: General overview of the LARA’s response Martin GRANIER 34 By using the Picking method of the AFDD MATLAB code [32], it is possible to select the four first modes to obtain the four first eigenfrequencies of both sensors. Figure 13: LARA’s response against Earthquake 1 excitation Figure 14: Commercial peaks of frequencies selected for “Earthquake1” Figure 15: LARA’s peaks of frequencies selected for “Earthquake1” Martin GRANIER 35 The visual response presents great similarities but it has to be verified by calculating the ARE and the MAC. Earthquake 1 Mode number Commercial (Hz) LARA (Hz) Relative Error (%) 1 3,12 3,03 2,84% 2 9,35 9,42 0,76% 3 13,64 13,80 1,17% 4 24,55 24,56 0,07% The table confirms the first sight by showing that the four first eigenfrequencies are very similar. Indeed, they differ from a maximum of 2,84%. Furthermore, the MAC is computed and confirms even more the similarities between the two responses of both sensors. Earthquake1 Mode Shape Commercial Mode Shape LARA MAC -1 -0,808 -0,498 -0,048 -1 -0,822 -0,493 -0,072 0,9971 -0,769 0,354 1 0,012 -0,800 0,380 1 0,010 -0,504 1 -0,779 -0,008 -0,485 1 -0,744 0,015 -0,012 -0,031 0,124 -1 -0,110 -0,073 0,070 -1 5.1.2 Earthquake 2 The same procedure is used to obtain the results of the “Earthquake2”, from 9:46:10 (UTC+7) to 9:46:23 (UTC+7). Table 5: 4 first eigenfrequencies of the sensors during “Earthquake1” Table 6: 4 first mode shapes of the sensors during “Earthquake1” Figure 16: LARA’s response against “Earthquake2” excitation Martin GRANIER 36 Again, the first sight seems to be very similar for both graphs. To verify it, the ARE and the MAC are calculated as follows. Earthquake 2 Mode number Commercial (Hz) LARA (Hz) Relative Error (%) 1 3,12 3,36 7,95% 2 9,35 9,42 0,76% 3 13,64 13,80 1,17% 4 15,97 15,93 0,30% The table confirms the first sight by showing that the four first eigenfrequencies are very similar. However, the first eigenfrequency differs by 7,95%. We will try to explain that difference later. Table 7: 4 first eigenfrequencies of the sensors during “Earthquake2” Figure 17: Commercial peaks of frequencies selected for “Earthquake2” excitation Figure 18: LARA’s peaks of frequencies selected for “Earthquake2” excitation Martin GRANIER 37 Furthermore, the MAC is computed and confirms even more the similarities between the two responses of both sensors. Earthquake2 Mode Shape Commercial Mode Shape LARA MAC -1 -0,802 -0,482 -0,023 -1 -0,824 -0,469 -0,003 0,9961 -0,768 0,348 1 0,031 -0,794 0,368 1 0,048 -0,501 1 -0,771 -0,024 -0,478 1 -0,791 0,014 -0,085 0,252 -0,528 1 -0,120 0,381 -0,614 1 5.1.3 Sine 1 As well as the two first cases, the same procedure is used to obtain the results of the “Sine1”, from 9:48:34 (UTC+7) to 9:48:46 (UTC+7). Table 8: 4 first mode shapes of the sensors during “Earthquake2” Figure 19: LARA’s response against “Sine1” excitation Figure 20: Commercial peaks of frequencies selected for “Sine1” excitation Martin GRANIER 38 To complete the comparison, the ARE and the MAC are calculated as follows. Sine1 Mode number Commercial (Hz) LARA (Hz) Relative Error (%) 1 1,17 1,01 13,64% 2 3,12 3,36 7,95% 3 8,96 9,08 1,38% 4 14,03 13,80 1,64% Sine 1 Mode Shape Commercial Mode Shape LARA MAC -1 -0,940 -0,955 -0,888 -1 -0,981 -0,948 -0,896 0,9972 -1 -0,801 0 -0,020 -1 -0,812 0 -0,011 -0,773 0 1 0,195 -0,799 0 1 0,185 -0,477 1 -0,909 0 -0,483 1 -0,782 0 5.1.4 Sine 2 As well as the three first cases, the same procedure is used to obtain the results of the “Sine2”, from 9:51:16 (UTC+7) to 9:51:30 (UTC+7). Table 9: 4 first eigenfrequencies of the sensors during “Sine1” Table 10: 4 first mode shapes of the sensors during “Sine1” Table 8: 4 first mode shapes of the sensors during “Earthquake2” Figure 21: LARA’s peaks of frequencies selected for “Sine1” excitation Martin GRANIER 39 Figure 22: LARA’s response against “Sine2” excitation Figure 23: Commercial peaks of frequencies selected for “Sine2” excitation Figure 24: LARA’s peaks of frequencies selected for “Sine2” excitation Martin GRANIER 40 Below will be presented the tables of ARE and MAC values. Sine2 Mode number Commercial (Hz) LARA (Hz) Relative Error (%) 1 1,17 1,01 13,64% 2 3,12 3,36 7,95% 3 9,35 9,42 0,76% 4 14,03 13,80 1,64% Sine 2 Mode Shape Commercial Mode Shape LARA MAC -1 -0,939 -0,949 -0,878 -1 -0,977 -0,945 -0,908 0,995 -1 -0,804 0 -0,021 -1 -0,811 0 -0,004 -0,768 0 1 0,053 -0,790 0 1 0,054 -0,477 1 -0,891 0 -0,480 1 -0,796 0 5.1.5 Sine 3 As well as the four first cases, the same procedure is used to obtain the results of the “Sine3”, from 9:54:03 (UTC+7) to 9:55:50 (UTC+7). Table 11: 4 first eigenfrequencies of the sensors during “Sine2” Table 12: 4 first mode shapes of the sensors during “Sine2” Figure 25: LARA’s response against “Sine3” excitation Martin GRANIER 41 Below will be presented the tables of ARE and MAC values. 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Martin GRANIER 51 Appendices Appendix A: Technical sheet LARA sensor Item Description Type or Model MEMS accelerometer /Inclinometer Dimension 40 x 40 x 5mm Measurement Range as accelerometer ± 2.0 g* Noise density as accelerometer 51µg/√Hz Resolution as accelerometer 31µg Frequency Response as accelerometer 0 – 61Hz Sampling Rate as accelerometer 333 Hz Sensitivity as accelerometer 625 mV/g Measurement range (degrees) as inclinometer 0-4o Precision (degrees) as inclinometer Up to 0.002 degrees in Static mode 0.02 degrees in Dynamic mode Sampling rate as inclinometer Up to 333 Hz Operating temperature -40oC to +85oC Communication Ethernet or USB Power Source Ethernet or USB Power Consumption 200mA @ 5V Waterproof IP67 compliant Martin GRANIER 52 Appendix B: Technical sheet PCB 3713B112G sensor Martin GRANIER 53 Appendix C: Matlab code “Timeselecting” Appendix D: Matlab code “Compute_MAC”