A sensing paradigm of analog-to-feature (A2F) based on the MEMS accelerometer-integrated reservoir computing

A sensing paradigm of analog-to-feature (A2F) based on the MEMS accelerometer-integrated reservoir computing | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article A sensing paradigm of analog-to-feature (A2F) based on the MEMS accelerometer-integrated reservoir computing Xudong Zou, Wuhao Yang, Jie Sun, Xiaowei Guo, Xingyin Xiong, Zheng Wang, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4343664/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The current boom in Micro-electromechanical Systems combined with the advent of the physical reservoir computing make it possible to break through the bottleneck of traditional sensing paradigms based on physically separated sensors and processors. Here, we report a pioneering work on a novel sensing paradigm of analog-to-feature using a stiffness modulated micromechanical resonant accelerometer. Specifically, the amplitude-acceleration nonlinearity of the accelerometer and its transient nonlinearity serve as the nonlinear dynamics of our physical reservoir computing to categorize the accelerometer input. Furthermore, we perform ten times tenfold cross-validation tests and use the confusion matrix to test its classification performance on a data set of the different acceleration corresponding to the different motion postures generated by a six-axis IMU. The results show a classification accuracy of 97.33%, which proves that our MEMS accelerometer-integrated reservoir computing enables data processing ability locally at the sensing side for efficient distributed processing. Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Over recent decades, sensing technology has been considered an important information processing technology in modern society, which has witnessed prodigious success and spawned a lot of new technologies and applications 1,2 , such as the Internet of Things (IoT) 3,4 and ubiquitous sensing 5,6 . With the rapid development of these emerging fields, the massive raw data generated by a plethora of sensor nodes is consuming more and more transmission bandwidth, storage capacity, and energy, which calls for systems capable of “Edge Computing” to process a deluge of information locally efficiently with low power consumption 7 . This ability to process information locally appears poised to become increasingly important in the continuing development of various technologies and applications including machine learning, artificial intelligence (AI) and IoT 8,9 . However, current edge computing systems mostly rely on physically separated sensors and digital processing units, leading to a high rate of energy consumption and long-time latencies when digitizing the analog signals followed by digital feature extraction and classification due to the limitation of the Nyquist rate 10 . On account of this, the sensing paradigm based on the current edge computing is still challenging to be compatible with the ever-increasing demand for transmission bandwidth and energy efficiency in the IoT era. Therefore, new insights into the sensing paradigm based on current edge devices are urgently needed. Inspired by an acquisition method thought for IoT devices, a promising way to circumvent the above limitation is an alternative sampling technique called Analog-to-Feature (A2F) conversion that directly acquires features in the analog domain instead of traditional sensor digitization strategies 11 . Due to the unique way of directly extracting useful information only in the analog domain, it has been proven to harbor enormous potential to significantly improve the transmission bandwidth and energy efficiency of signal processing in various applications 12–14 . But most A2F methods reported in the literature are designed for specific application such as signal recovery, rather than classification tasks, which suffers from noise folding and poor feature extraction accuracy 12,13,15 . The current boom in Micro-electromechanical Systems (MEMS) combined with the advent of the physical reservoir computing (PRC) provide new ideas for A2F method based on the MEMS edge sensors. Reservoir computing (RC) is a prospective neuromorphic paradigm for promoting this disruptive application owing to its well-known low training cost and compatibility with hardware, which offers efficient processing capability for temporal information by extracting features from a temporal input into a higher-dimension feature space 16,17 . This feature extraction is carried out by the dynamics of a nonlinear system with fixed-weight connections, called a reservoir. Moreover, the fixed reservoir without adaptive updating is amenable to hardware implementation using various nonlinear dynamical systems 18 , such as electronics 19,20 , optoelectronics 21–24 , spintronics 25–27 , electrochemical systems 28,29 , memristors 7,30–32 , and MEMS devices 33–39 . Therein, MEMS-based RC serves the dual abilities of sensing and computing for various force stimuli (accelerations, sound pressure, etc.), which make it a promising candidate for smart sensors with the capability of edge computing 33,35,40 . Particularly, RC implemented in MEMS resonator is expected to further eliminate the need for the interface between sensing and computing, because physical stimuli can be directly fed into the dynamics of the reservoir, thus serving as a platform to realize A2F based on PRC. In this work, we focus on a novel non-delayed PRC structure we demonstrated previously 36 and propose a new sensing paradigm based on its implementation in a stiffness modulated MEMS resonant accelerometer 41–43 to achieve analog-to-feature conversion for the signals that accelerometer sensed. Previously, we have systematically studied the nonlinear behavior of the MEMS resonant accelerometer 44 , and shown the potential to realize efficient PRC by harnessing their rich nonlinear dynamics 36 . The frequency-acceleration nonlinearity is not available because a fixed drive frequency is needed for the non-delayed PRC we proposed. To be favorably leveraged to generate rich nonlinear dynamics needed, we focus on the amplitude-acceleration nonlinearity of the MEMS accelerometer and carry out the simulation analysis and experimental characterization. Furthermore, we implement the non-delayed PRC using the MEMS resonant accelerometer with the hybrid nonlinearity that is composed of amplitude-acceleration nonlinearity and transient nonlinearity. To realize the classification for the temporal acceleration input that causes the perturbation of the axial stiffness, we build a data set of the different accelerations corresponding to the different motion postures using a six-axis IMU. Then we perform ten times tenfold cross-validation tests and use the confusion matrix to test the classification performance of the non-delayed PRC we proposed on this data set. The results demonstrate a classification accuracy of 97.33%, which preliminarily show the feasibility of MEMS accelerometer-integrated RC with edge computing capability by using stiffness variation input. Moreover, we also discussed the relationship between the performance of the PRC and the intrinsic nature of the stimuli that the MEMS accelerometer sensed. These results as well as the meaningful discussion provide a foundation for the MEMS-based PRC and facilitate the disruptive applications using smart sensors with edge computing in the future IoT era. Results Concept of the sensing paradigm of A2F based on PRC In conventional sensing paradigm, the signal feature extraction for classification tasks usually relies on physically separated sensing part and processing part. The sensing part usually consists of specific sensors that are only responsible for signal acquisition, while the signal feature extraction also requires a series of analog signal pre-processing (filtering, noise reduction, normalization, etc.), time-frequency domain transformation, analog-to-digital conversion (ADC), and computing in the processing part, as schematically illustrated in Fig. 1 a. This physically separated sensing and processing paradigm inevitably imposes a heavy burden on transmission bandwidth and power consumption. In this work, we use a stiffness modulated differential resonant accelerometer with two identical resonators as an edge device to execute the signal acquisition and processing, which significantly reduces data transfer and simplifies the system structure, as schematically illustrated in Fig. 1 b and Fig. 1 c. The accelerometer can respond to the acceleration perturbation along its sensitive direction by the proof mass, which changes the axial stiffness of the resonant beams connected to the proof mass by micro-leverage structures. The change in axial stiffness causes a shift in the resonance frequency of the resonant beam, which is usually detected by a closed-loop interface circuit. Then the acceleration can be calculated by the relationship between the acceleration and the frequency shift. Meanwhile, we utilize its inherent nonlinearity and short-term memory characteristics to build a physical reservoir to realize feature extraction and classification for analog input 36 , which is referred to as Analog-to-Feature (A2F) conversion. Owing to the superiority of the physical reservoir without adaptive updating in training and the feasibility of designing a reservoir using a micromechanical resonator with nonlinear dynamics, the reservoir-based sensing paradigm of A2F can serve as an ideal candidate for a near-sensor or edge computing paradigm with high speed, low cost, and energy efficient. For another resonator in this differential resonant accelerometer, we use it to monitor the actual acceleration input corresponding to the calibrated electrostatic force input, as shown in Fig. 1 d. The nonlinear dynamics of the stiffness modulated MEMS accelerometer As the key device that serves the dual purpose of sensing and processing for the reservoir-based sensing paradigm, the differential resonant accelerometer with specially designed sensitivity enhancing structure and tuning structure has been reported in our previous work 41–43 , as schematically illustrated in Fig. 1 C. The details of the fabrication and the size information for the device is shown in Materials and Methods part. Here, we focus on its nonlinear dynamics that are crucial to the physical reservoir. The sensitive beam connected to the proof mass can be simplified as a second-order mass-damper-spring system, whose motion equation can be written as, $${m}_{r}\ddot{z}+c\dot{z}+\left({k}_{m}+{k}_{axial}\right)z+{k}_{m3}{z}^{3}=\frac{1}{2}\frac{{C}_{0}d}{{\left(d-z\right)}^{2}}{\left({V}_{dc}+{V}_{ac}\text{cos}{\omega }_{d}t\right)}^{2}-\frac{1}{2}\frac{{C}_{0}d}{{\left(d+z\right)}^{2}}{\left({V}_{dc}\right)}^{2}$$ 1 where \(z,\dot{z},\ddot{z}\) are the displacement, velocity and acceleration of the resonant beam in transverse motion, respectively, \({m}_{r}\) is the effective mass of the resonant beam, \(c=\frac{{m}_{r}{w}_{n}}{Q}\) is the equivalent damping coefficient, \({k}_{m}\) is the linear stiffness parameter, \({k}_{axial}\) is the axial stiffness perturbation caused by the external acceleration, \({k}_{m3}\) is the nonlinear (cubic) stiffness parameter, \(d,{C}_{0}\) are the initial distance and the corresponding capacitance between the resonant beam and electrode, respectively, \({V}_{dc}\) is the bias voltage applied on the resonant beam, \({V}_{ac},{\omega }_{d}\) are the amplitude and angular frequency of the driven signal for the resonant beam. According to our previous work 36 , a specifically designed resonant beam exhibits hybrid nonlinear dynamics including the duffing nonlinearity and the intrinsic transient exponential nonlinear response characteristics when it is seen as a typical underdamped second-order oscillation system, which guarantees the dynamic nonlinear features and fading memory of the reservoir. Thanks to the complex nonlinear phenomena caused by the scale effect and fabrication tolerance in the MEMS resonant accelerometers, the nonlinear dynamics of the resonant frequency and amplitude of the resonant beams with the external acceleration can act as a physical reservoir able to map temporal inputs into a feature space that can be analyzed by a trained readout layer. Figure 2 a shows the simulation result for the frequency shift (delta-f = f-f0) dependent dynamical nonlinearity of the resonant beam with the external acceleration input. Figure 2 b shows the simulation result for the amplitude dependent dynamical nonlinear hysteresis of the resonant beam with the external acceleration input, which is similar to the electrostatic spring softening effect in the duffing nonlinearity. As we all know, the hysteresis region between the two bifurcation points ([a=-54g, a=-1g]) reserves complex nonlinear dynamics. But as an edge sensor, the differential resonant accelerometer should be driven to an appropriate nonlinear region to ensure not only the nonlinear transformation of the input signal, but also the stable sensing of the external acceleration. Considering the resonant frequency of the resonant beam needs to be tracked and locked by a Phase Lock Loop (PLL), which is incompatible with the frequency detection through the closed-loop interface circuit. Therefore, we use the nonlinear response between the amplitude of the resonant beam and the external acceleration as the reservoir dynamics in this work. The grey region represents the optimal dynamic range of the input acceleration for our system, which corresponds to the classification accuracy over 90% for different motion postures, as shown in Fig. 2 d. Experimentally, we use electrostatic force instead of the external acceleration to perturbate the stiffness of the resonant beam to verify the dynamical nonlinearity of the device. The simulation and experimental results are shown in the Fig. 2 c. . The experimental setup for the PRC with a stiffness modulated accelerometer The differential resonant accelerometer is packaged and integrated on a printed circuit board (PCB), which is driven by the electrostatic force instead of the external acceleration, and detected by an interface circuit, as shown in Fig. 3 b and c . To calibrate the external acceleration dependent electrostatic force, we fix the PCB with the packaged accelerometer on a triaxial rotating stage, and simulate the acceleration of ± 1g by changing the orthogonal position between gravity and the sensitive axis, as shown in Fig. 3 a. A lock-in amplifier (Zurich Instruments MFLI500kHz/5MHz) is used to sweep frequency and detect the frequency shift. A power source (Keysight U8032A ) is used to apply electrostatic force to equilibrate the gravity. Results show that the electrostatic force corresponding to the 27.6V DC voltage is equal to the inertial force generated by 1g acceleration, as shown in Fig. 2 c. Figure 3 d shows the optical microscopy image of the differential resonant accelerometer with a scale bar of 1 mm. The comb driving structure, clamped-clamped beam structure, and micro lever structure are highlighted in red dotted frames 1, 2, 3, respectively, which correspond to the SEM images Fig. 3 e, Fig. 3 f, and Fig. 3 g. The classification for the acceleration input via the MEMS accelerometer-integrated RC As a novel physical reservoir without digital operation such as delay and mask, the designed resonant beam with hybrid nonlinear dynamics has shown excellent performance on feature extraction and classification based on some standard benchmarks 36 . In this work, we migrate this novel physical reservoir on the differential resonant accelerometer to make it an edge sensor. The priority is to verify its performance for the acceleration input corresponding to the different motion postures by the customized dataset acquired from a homemade six-axis IMU sensor, which is elaborated in our previous work 36 . Figure 4 a shows the different acceleration waveforms in the time domain corresponding to the 8 motion postures, including “Jump”, “Walk”, “Jog”, “Squat”, “Stretch”, “ChestE”, “ArmC”, and “BodyC. Thanks to the nonlinear dynamical mechanism that stiffness perturbation caused by the external acceleration and the non-delay architecture without mask operation in the digital domain, the input acceleration can be directly fed into the dynamics of the reservoir and be classified by feature extraction from the analog domain with low power consumption. Figure 4 b shows the color block diagram for the results of the different features corresponding to the 8 motion postures extracted by the nonlinear transformation of our MEMS accelerometer-integrated RC. We perform ten times tenfold cross-validation tests and use the confusion matrix to characterize the classification performance on the customized dataset for motion posture recognition. Each sample of the test dataset is divided into 15 groups and tested by ten times. Results show a classification accuracy of (97.33 ± 0.136)%, as shown in Fig. 4 c. A box plot inset displays the discrete distribution of the data. Figure 4 d shows the results of the false-color confusion matrix. The color bar represents the number of samples whose predicted result are consistent with the target result. The power consumption of the core device including the accelerometer and its driving interface circuit in our prototype system is estimated to be less than 300 ± 1mW, as shown in Fig. 3 . In our experimental setup, the power consumption of the interface circuit is approximated by Pc = 5V×0.06A = 300mW, while the power consumption of the differential resonant accelerometer is approximated by Pa = 100mV×0.01A + 10V×0.01uA = 1mW. Discussion MEMS resonant accelerometer exhibits rich nonlinear behaviors under large displacement oscillations, originating from the micro-scale effects, the intrinsic geometrical nonlinearity as well as the coupling effects of the multiple physical fields and so on. Although these nonlinearities limit the resolution and dynamic range for the acceleration measurement, they generate rich nonlinear dynamics required for the MEMS accelerometer-integrated RC, which makes it possible to efficiently process the temporal acceleration input that is sensed by the accelerometer. For instance, when the resonant beam is perturbed by a sufficiently large input acceleration through the proof mass and the micro lever structure connected to it, the accelerometer exhibits frequency-acceleration nonlinearity and the amplitude-acceleration nonlinearity. But the frequency-acceleration nonlinearity is not available because a fixed drive frequency is needed for the non-delayed PRC we proposed. Thus, we focus on the amplitude-acceleration nonlinearity as well as its intrinsic transient nonlinearity, and use this hybrid nonlinearity to implement the MEMS accelerometer-integrated RC. Besides, the mechanism that stiffness perturbation caused by the external acceleration allows the input acceleration to be directly fed into the dynamics of the reservoir and to be classified by feature extraction from the analog domain with low power consumption. Considering both of the two identical resonators of the differential resonant accelerometer possess the dual capabilities of sensing and computing, the sensing paradigm we proposed can provide more edge computing modes in future improvement. Except for the sensing mode or the reservoir computing mode, the differential resonant accelerometer can also realize the classification and recognition for a selected piece of acceleration input by applying the two resonators simultaneously, one serving as a threshold switch for acceleration signal monitoring and the other for information processing. In summary, we implement a novel sensing paradigm based on a novel non-delayed PRC structure we demonstrated previously using a stiffness modulated MEMS resonant accelerometer. and investigate the structure that converts the acceleration into axial tension to be added to the resonator dynamics. Furthermore, we investigate the nonlinear behavior of the MEMS resonant accelerometer and use the hybrid nonlinearity that is composed of amplitude-acceleration nonlinearity and transient nonlinearity to implement the non-delayed PRC. Moreover, we build a data set of the different accelerations corresponding to the different motion postures using a six-axis IMU to study the processing performance for the acceleration that causes the perturbation of the axial stiffness of the resonator dynamics. The results of the ten times tenfold cross-validation and the confusion matrix show a classification accuracy of 97.33%, which proves that our MEMS accelerometer-integrated RC enables data processing ability locally at the sensing side for efficient distributed processing. Additionally, these results also overcome the bottleneck of the traditional sensing paradigm relied on discrete sensors and physically separated processing units, where analog-to-digital conversion units between sensing and computing are indispensable, thus having the potential to improve the energy efficiency of information processing. This energy efficient method also facilitates the new future possibilities for exploring the emerging applications of the A2F in MEMS-based PRC. Methods Device fabrication details The MEMS differential resonant accelerometer is fabricated using the silicon micro-manufacture technology based on the standard Silicon on Insulator (SOI) micromachining process and multilayer silicon wafer bonding process. The fabrication process starts with a 6-inch SOI wafer (device thickness of 50µm, oxide thickness of 1µm, the substrate thickness of 380µm) with a pre-etched shallow trench. The bottom electrodes are defined by the patterned silicon that is isolated from each other by etching to expose the buried oxide (BOX) layer. Followed by the silicon-to-silicon bonding process to bond the second SOI wafer upside down to the predefined silicon electrodes after depositing the bond-plane silicon dioxide. Then remove the BOX layer and the substrate silicon of the second SOI, and define the top silicon electrodes by deep reactive ion etching (DRIE). Finally, bond a cap silicon wafer with etched cavities and deposit getter material to the aforementioned bond-plane silicon dioxide using the glass frit wafer bonding to achieve wafer-level hermetic packaging Device structure details The schematic illustration of the MEMS differential resonant accelerometer is shown in Fig. 1 (C). Two identical resonant beams are connected to the suspended proof mass by micro-levers to amplify the acceleration induced inertial force. The thickness of the resonant beam and the suspended proof mass is 50µm, which depends on the device layer thickness of the SOI wafer. The suspended proof mass is about 4.269×10^(-6) kg. The length and width of the resonant beam are designed based on the appropriate resonant frequency and quality factor for the MEMS accelerometer-integrated RC obtained by finite element simulation and the limitation of the fabrication. The length of the resonant beam is 400 µm, and the width of the resonant beam is 6 µm Declarations Contributions All authors participated in the scientific discussion. W.Y., J.S., and X.Z. conceived the idea. J.S. and W.Y. carried out most of the experiments, and W.Y. wrote the manuscript. W.Y. and J.S. equally contributed to this work. X.Z. and W.Y. provided the know-how and the concept of the proposed sensing paradigm of analog-to-feature (A2F). X.G. helped in the simulation and the measurement. X.G., X.X and Z.W analyzed the nonlinear behavior. X.X and Z.W helped in the design and the fabrication for the MEMS resonant accelerometer. Z.L and X.B attended the discussion and all authors participated in the revision of the manuscript. Acknowledgements (optional) The authors would like to thank the members of the State Key Laboratory of Transducer Technology for helpful discussions. This research was partially supported by National Key Research and Development Program of China under Grant No. 2023YFB3207901, the National Natural Science Foundation of China (Grant No. 61971399), and the Key Research Program of Frontier Science (CAS, Grant No. ZDBS-LY-JSC028). Ethics declarations Competing interests The authors declare that they have no competing interests. References Khoshnoud, F., de Silva, C. W. J. I. I. & Magazine, M. Recent advances in MEMS sensor technology-mechanical applications. 15 , 14-24 (2012). Bogue, R. J. S. r. Recent developments in MEMS sensors: A review of applications, markets and technologies. 33 , 300-304 (2013). Al-Fuqaha, A. et al. Internet of things: A survey on enabling technologies, protocols, and applications. 17 , 2347-2376 (2015). Atzori, L., Iera, A. & Morabito, G. J. C. n. The internet of things: A survey. 54 , 2787-2805 (2010). Essa, I. A. J. I. p. c. Ubiquitous sensing for smart and aware environments. 7 , 47-49 (2000). 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Xiong, X. et al. Using electrostatic spring softening effect to enhance sensitivity of MEMS resonant accelerometers. 21 , 5819-5827 (2020). Cai, P., Xiong, X., Wang, K., Wang, J. & Zou, X. J. M. An improved difference temperature compensation method for MEMS resonant accelerometers. 12 , 1022 (2021). Zou, X. & Seshia, A. A. J. I. S. J. Non-linear frequency noise modulation in a resonant MEMS accelerometer. 17 , 4122-4127 (2017). Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4343664","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":307813334,"identity":"6f1ebeac-84b2-4c8b-8f40-32b13c4e4319","order_by":0,"name":"Xudong Zou","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxElEQVRIiWNgGAWjYLACngoGHlK1nCFZC28bKarl23vMJN7Os5Mxbz/8+ANDjR0D/+wG/FoYe84YG87dlswjcybNTILhWDKDxJ0D+LUwS+QYPubdxswjIcFgxsDAdoDBQCIBvxY2iRyDw7xz6oFa2D9/YPhHhBYesC0Nh4FaeAwkGNuI0CLBc6zYcM6x4zwSPDllEol9yTwSNwhokW9v3ibxpqbaXoL9+OYPH77ZyfHPIKAFFQAVkxqno2AUjIJRMAqwAQBAADVoaEIWHQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-5347-0124","institution":"Aerospace Information Research Institute","correspondingAuthor":true,"prefix":"","firstName":"Xudong","middleName":"","lastName":"Zou","suffix":""},{"id":307813335,"identity":"59b66a18-f68f-4cd0-ae09-01eb9b5c4860","order_by":1,"name":"Wuhao Yang","email":"","orcid":"","institution":"The State Key Laboratory of Transducer Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing","correspondingAuthor":false,"prefix":"","firstName":"Wuhao","middleName":"","lastName":"Yang","suffix":""},{"id":307813336,"identity":"9db20b37-e392-444e-926d-37c306b435c0","order_by":2,"name":"Jie Sun","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Jie","middleName":"","lastName":"Sun","suffix":""},{"id":307813337,"identity":"befecd4d-a877-4142-ad87-5e15797a6650","order_by":3,"name":"Xiaowei Guo","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Xiaowei","middleName":"","lastName":"Guo","suffix":""},{"id":307813338,"identity":"f4a009e9-27f5-47ef-aeb4-ca1596e96cde","order_by":4,"name":"Xingyin Xiong","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Xingyin","middleName":"","lastName":"Xiong","suffix":""},{"id":307813339,"identity":"7ca117eb-1dbf-418c-bc08-a661afb79a6b","order_by":5,"name":"Zheng Wang","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Zheng","middleName":"","lastName":"Wang","suffix":""},{"id":307813340,"identity":"f531f12a-8777-4843-865f-4952c35a3c70","order_by":6,"name":"Zhitian Li","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Zhitian","middleName":"","lastName":"Li","suffix":""},{"id":307813341,"identity":"e76e43a4-6ca3-4d07-9ca6-368b111bf1c5","order_by":7,"name":"Xiaorui Bie","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Xiaorui","middleName":"","lastName":"Bie","suffix":""}],"badges":[],"createdAt":"2024-04-29 14:51:42","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4343664/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4343664/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":58104343,"identity":"69593da5-d79e-456d-8bc8-248e9c41549d","added_by":"auto","created_at":"2024-06-11 07:19:28","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":643144,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eConceptual Schematic diagram of the sensing paradigm of analog-to-feature (A2F) based on the physical reservoir computing using a stiffness modulated micromechanical accelerometer\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e Conventional sensing paradigm based on physically separated sensors and digital processing units. Data features are typically extracted through a series of analog signal pre-processing, analog-to-digital conversion (ADC), and post-processing in the processing part. \u003cstrong\u003eb\u003c/strong\u003e The sensing paradigm of analog-to-feature (A2F) based on the physical reservoir computing using a stiffness modulated micromechanical accelerometer. With the inherent nonlinearity and fading memory, the physical reservoir can nonlinearly transform the input data and extract the temporal features, then map them to a high-dimensional space for a trained readout function to implement high-level processing such as classification and prediction. \u003cstrong\u003ec\u003c/strong\u003e Schematic icons of the 8 motion postures in the customized dataset acquired from a homemade six-axis IMU sensor, including “Jump”, “Walk”, “Jog”, “Squat”, “Stretch”, “ChestE(xtention)”, “ArmC(ircle)”, and “BodyC(ircle). \u003cstrong\u003ed\u003c/strong\u003e Illustration of the sensing paradigm of A2F implemented on a stiffness modulated differential resonant accelerometer that serves as an edge sensor for sensing and signal processing, enabling the extraction of temporal features such as the categorization of acceleration. One of the resonators serves the dual purpose of sensing and computing, while the other serves as a monitor for the acceleration input.\u003c/p\u003e","description":"","filename":"Fig.1.png","url":"https://assets-eu.researchsquare.com/files/rs-4343664/v1/de50802430067ea2453bad51.png"},{"id":58104344,"identity":"a67c0fd1-f04d-4276-9d1c-e6c835f4d55a","added_by":"auto","created_at":"2024-06-11 07:19:28","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":262132,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe nonlinear dynamics of the stiffness modulated MEMS accelerometer.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e The simulation result for the frequency dependent dynamical nonlinearity of the resonant beam. \u003cstrong\u003eb\u003c/strong\u003e The simulation result for the amplitude dependent dynamical nonlinearity of the resonant beam. The grey region shows the optimal dynamic range of the input acceleration for our system. \u003cstrong\u003ec\u003c/strong\u003e The experimental calibration of the external acceleration dependent electrostatic force, which is used to drive the accelerometer in the classification task for different motion postures. \u003cstrong\u003ed \u003c/strong\u003eThe simulation result of the classification accuracy versus the input acceleration that corresponds to different motion postures. “Afactor” represents the calculated driving voltage of the electrostatic force corresponding to the external acceleration.\u003c/p\u003e","description":"","filename":"Fig.2.png","url":"https://assets-eu.researchsquare.com/files/rs-4343664/v1/c079543a438291d52823cd06.png"},{"id":58104716,"identity":"ff8486b9-7cfe-4624-884e-6b5a135ef525","added_by":"auto","created_at":"2024-06-11 07:27:28","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":4101677,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe experimental setup for the PRC with a stiffness modulated accelerometer.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e The calibration set up for the acceleration dependent electrostatic force. \u003cstrong\u003eb\u003c/strong\u003eThe closed-loop oscillating circuit for monitoring the actual acceleration input corresponding to the calibrated electrostatic force input. \u003cstrong\u003ec\u003c/strong\u003e A zoomed view for the red dotted frame in \u003cstrong\u003ea\u003c/strong\u003e, which indicates the PCB with the packaged accelerometer. \u003cstrong\u003ed\u003c/strong\u003e The optical microscopy image of the differential resonant accelerometer with red dotted frames 1, 2, 3 highlights the comb driving structure, clamped-clamped beam structure, and micro lever structure, respectively, which correspond to the SEM images \u003cstrong\u003ee\u003c/strong\u003e, \u003cstrong\u003ef\u003c/strong\u003e, and \u003cstrong\u003eg\u003c/strong\u003e.\u003c/p\u003e","description":"","filename":"Fig.3.png","url":"https://assets-eu.researchsquare.com/files/rs-4343664/v1/0b6ad14a524249937b4509bb.png"},{"id":58104346,"identity":"53cd500f-bfac-4535-ad47-16adeb872401","added_by":"auto","created_at":"2024-06-11 07:19:28","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":211242,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExperimental results on the customized dataset for motion posture recognition.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e The different acceleration waveforms in the time domain corresponding to the 8 motion postures, including “Jump”, “Walk”, “Jog”, “Squat”, “Stretch”, “ChestE”, “ArmC”, and “BodyC. \u003cstrong\u003eb\u003c/strong\u003e The color block diagram to represent the different features corresponding to the 8 motion postures extracted by the nonlinear transformation of our MEMS accelerometer-integrated RC. \u003cstrong\u003ec\u003c/strong\u003e The classification accuracy results of the ten times ten-fold cross-validation. The box plot inset shows the first and third quartiles (the bottom and the top of the box), the median (the red line in the box), 1.5 times the interquartile range (whisker), and the mean values in the ten times ten-fold cross-validation (circles). \u003cstrong\u003ed\u003c/strong\u003e The false-color confusion matrix corresponding to the predicted results in the ten times ten-fold cross-validation. The corresponding confusion matrices for the MEMS classifier. The rows show the target pattern of the motion postures and the columns show the predicted pattern of the motion postures. The color bar represents the number of correctly predicted samples.\u003c/p\u003e","description":"","filename":"Fig.4.png","url":"https://assets-eu.researchsquare.com/files/rs-4343664/v1/c15bcbc93f7139b93d9a7964.png"},{"id":59659312,"identity":"c0bb3d17-a334-4408-9039-48aec4baa8e0","added_by":"auto","created_at":"2024-07-04 11:29:53","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":7052669,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4343664/v1/986385b5-ba18-42ac-9e35-71c917b8223c.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"A sensing paradigm of analog-to-feature (A2F) based on the MEMS accelerometer-integrated reservoir computing","fulltext":[{"header":"Introduction","content":"\u003cp\u003eOver recent decades, sensing technology has been considered an important information processing technology in modern society, which has witnessed prodigious success and spawned a lot of new technologies and applications\u003csup\u003e1,2\u003c/sup\u003e, such as the Internet of Things (IoT)\u003csup\u003e3,4\u003c/sup\u003e and ubiquitous sensing\u003csup\u003e5,6\u003c/sup\u003e. With the rapid development of these emerging fields, the massive raw data generated by a plethora of sensor nodes is consuming more and more transmission bandwidth, storage capacity, and energy, which calls for systems capable of \u0026ldquo;Edge Computing\u0026rdquo; to process a deluge of information locally efficiently with low power consumption\u003csup\u003e7\u003c/sup\u003e. This ability to process information locally appears poised to become increasingly important in the continuing development of various technologies and applications including machine learning, artificial intelligence (AI) and IoT\u003csup\u003e8,9\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eHowever, current edge computing systems mostly rely on physically separated sensors and digital processing units, leading to a high rate of energy consumption and long-time latencies when digitizing the analog signals followed by digital feature extraction and classification due to the limitation of the Nyquist rate\u003csup\u003e10\u003c/sup\u003e. On account of this, the sensing paradigm based on the current edge computing is still challenging to be compatible with the ever-increasing demand for transmission bandwidth and energy efficiency in the IoT era. Therefore, new insights into the sensing paradigm based on current edge devices are urgently needed. Inspired by an acquisition method thought for IoT devices, a promising way to circumvent the above limitation is an alternative sampling technique called Analog-to-Feature (A2F) conversion that directly acquires features in the analog domain instead of traditional sensor digitization strategies\u003csup\u003e11\u003c/sup\u003e. Due to the unique way of directly extracting useful information only in the analog domain, it has been proven to harbor enormous potential to significantly improve the transmission bandwidth and energy efficiency of signal processing in various applications\u003csup\u003e12\u0026ndash;14\u003c/sup\u003e. But most A2F methods reported in the literature are designed for specific application such as signal recovery, rather than classification tasks, which suffers from noise folding and poor feature extraction accuracy\u003csup\u003e12,13,15\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe current boom in Micro-electromechanical Systems (MEMS) combined with the advent of the physical reservoir computing (PRC) provide new ideas for A2F method based on the MEMS edge sensors. Reservoir computing (RC) is a prospective neuromorphic paradigm for promoting this disruptive application owing to its well-known low training cost and compatibility with hardware, which offers efficient processing capability for temporal information by extracting features from a temporal input into a higher-dimension feature space\u003csup\u003e16,17\u003c/sup\u003e. This feature extraction is carried out by the dynamics of a nonlinear system with fixed-weight connections, called a reservoir. Moreover, the fixed reservoir without adaptive updating is amenable to hardware implementation using various nonlinear dynamical systems\u003csup\u003e18\u003c/sup\u003e, such as electronics\u003csup\u003e19,20\u003c/sup\u003e, optoelectronics\u003csup\u003e21\u0026ndash;24\u003c/sup\u003e, spintronics\u003csup\u003e25\u0026ndash;27\u003c/sup\u003e, electrochemical systems\u003csup\u003e28,29\u003c/sup\u003e, memristors\u003csup\u003e7,30\u0026ndash;32\u003c/sup\u003e, and MEMS devices\u003csup\u003e33\u0026ndash;39\u003c/sup\u003e. Therein, MEMS-based RC serves the dual abilities of sensing and computing for various force stimuli (accelerations, sound pressure, etc.), which make it a promising candidate for smart sensors with the capability of edge computing\u003csup\u003e33,35,40\u003c/sup\u003e. Particularly, RC implemented in MEMS resonator is expected to further eliminate the need for the interface between sensing and computing, because physical stimuli can be directly fed into the dynamics of the reservoir, thus serving as a platform to realize A2F based on PRC.\u003c/p\u003e \u003cp\u003eIn this work, we focus on a novel non-delayed PRC structure we demonstrated previously\u003csup\u003e36\u003c/sup\u003e and propose a new sensing paradigm based on its implementation in a stiffness modulated MEMS resonant accelerometer\u003csup\u003e41\u0026ndash;43\u003c/sup\u003e to achieve analog-to-feature conversion for the signals that accelerometer sensed. Previously, we have systematically studied the nonlinear behavior of the MEMS resonant accelerometer\u003csup\u003e44\u003c/sup\u003e, and shown the potential to realize efficient PRC by harnessing their rich nonlinear dynamics\u003csup\u003e36\u003c/sup\u003e. The frequency-acceleration nonlinearity is not available because a fixed drive frequency is needed for the non-delayed PRC we proposed. To be favorably leveraged to generate rich nonlinear dynamics needed, we focus on the amplitude-acceleration nonlinearity of the MEMS accelerometer and carry out the simulation analysis and experimental characterization. Furthermore, we implement the non-delayed PRC using the MEMS resonant accelerometer with the hybrid nonlinearity that is composed of amplitude-acceleration nonlinearity and transient nonlinearity. To realize the classification for the temporal acceleration input that causes the perturbation of the axial stiffness, we build a data set of the different accelerations corresponding to the different motion postures using a six-axis IMU. Then we perform ten times tenfold cross-validation tests and use the confusion matrix to test the classification performance of the non-delayed PRC we proposed on this data set. The results demonstrate a classification accuracy of 97.33%, which preliminarily show the feasibility of MEMS accelerometer-integrated RC with edge computing capability by using stiffness variation input. Moreover, we also discussed the relationship between the performance of the PRC and the intrinsic nature of the stimuli that the MEMS accelerometer sensed. These results as well as the meaningful discussion provide a foundation for the MEMS-based PRC and facilitate the disruptive applications using smart sensors with edge computing in the future IoT era.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eConcept of the sensing paradigm of A2F based on PRC\u003c/p\u003e\n\u003cp\u003eIn conventional sensing paradigm, the signal feature extraction for classification tasks usually relies on physically separated sensing part and processing part. The sensing part usually consists of specific sensors that are only responsible for signal acquisition, while the signal feature extraction also requires a series of analog signal pre-processing (filtering, noise reduction, normalization, etc.), time-frequency domain transformation, analog-to-digital conversion (ADC), and computing in the processing part, as schematically illustrated in Fig. \u003cspan\u003e1\u003c/span\u003ea. This physically separated sensing and processing paradigm inevitably imposes a heavy burden on transmission bandwidth and power consumption. In this work, we use a stiffness modulated differential resonant accelerometer with two identical resonators as an edge device to execute the signal acquisition and processing, which significantly reduces data transfer and simplifies the system structure, as schematically illustrated in Fig. \u003cspan\u003e1\u003c/span\u003eb and Fig. \u003cspan\u003e1\u003c/span\u003ec. The accelerometer can respond to the acceleration perturbation along its sensitive direction by the proof mass, which changes the axial stiffness of the resonant beams connected to the proof mass by micro-leverage structures. The change in axial stiffness causes a shift in the resonance frequency of the resonant beam, which is usually detected by a closed-loop interface circuit. Then the acceleration can be calculated by the relationship between the acceleration and the frequency shift. Meanwhile, we utilize its inherent nonlinearity and short-term memory characteristics to build a physical reservoir to realize feature extraction and classification for analog input\u003csup\u003e36\u003c/sup\u003e, which is referred to as Analog-to-Feature (A2F) conversion. Owing to the superiority of the physical reservoir without adaptive updating in training and the feasibility of designing a reservoir using a micromechanical resonator with nonlinear dynamics, the reservoir-based sensing paradigm of A2F can serve as an ideal candidate for a near-sensor or edge computing paradigm with high speed, low cost, and energy efficient. For another resonator in this differential resonant accelerometer, we use it to monitor the actual acceleration input corresponding to the calibrated electrostatic force input, as shown in Fig. \u003cspan\u003e1\u003c/span\u003ed.\u003c/p\u003e\n\u003cp\u003eThe nonlinear dynamics of the stiffness modulated MEMS accelerometer\u003c/p\u003e\n\u003cp\u003eAs the key device that serves the dual purpose of sensing and processing for the reservoir-based sensing paradigm, the differential resonant accelerometer with specially designed sensitivity enhancing structure and tuning structure has been reported in our previous work\u003csup\u003e41\u0026ndash;43\u003c/sup\u003e, as schematically illustrated in Fig. \u003cspan\u003e1\u003c/span\u003eC. The details of the fabrication and the size information for the device is shown in Materials and Methods part. Here, we focus on its nonlinear dynamics that are crucial to the physical reservoir. The sensitive beam connected to the proof mass can be simplified as a second-order mass-damper-spring system, whose motion equation can be written as,\u003c/p\u003e\n\u003cdiv id=\"Equ1\"\u003e\n \u003cdiv id=\"FileID_Equ1\" name=\"EquationSource\"\u003e$${m}_{r}\\ddot{z}+c\\dot{z}+\\left({k}_{m}+{k}_{axial}\\right)z+{k}_{m3}{z}^{3}=\\frac{1}{2}\\frac{{C}_{0}d}{{\\left(d-z\\right)}^{2}}{\\left({V}_{dc}+{V}_{ac}\\text{cos}{\\omega }_{d}t\\right)}^{2}-\\frac{1}{2}\\frac{{C}_{0}d}{{\\left(d+z\\right)}^{2}}{\\left({V}_{dc}\\right)}^{2}$$\u003c/div\u003e\n \u003cdiv\u003e1\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cspan\u003e\u003cspan\u003e\\(z,\\dot{z},\\ddot{z}\\)\u003c/span\u003e\u003c/span\u003e are the displacement, velocity and acceleration of the resonant beam in transverse motion, respectively, \u003cspan\u003e\u003cspan\u003e\\({m}_{r}\\)\u003c/span\u003e\u003c/span\u003e is the effective mass of the resonant beam, \u003cspan\u003e\u003cspan\u003e\\(c=\\frac{{m}_{r}{w}_{n}}{Q}\\)\u003c/span\u003e\u003c/span\u003e is the equivalent damping coefficient, \u003cspan\u003e\u003cspan\u003e\\({k}_{m}\\)\u003c/span\u003e\u003c/span\u003e is the linear stiffness parameter, \u003cspan\u003e\u003cspan\u003e\\({k}_{axial}\\)\u003c/span\u003e\u003c/span\u003e is the axial stiffness perturbation caused by the external acceleration, \u003cspan\u003e\u003cspan\u003e\\({k}_{m3}\\)\u003c/span\u003e\u003c/span\u003e is the nonlinear (cubic) stiffness parameter, \u003cspan\u003e\u003cspan\u003e\\(d,{C}_{0}\\)\u003c/span\u003e\u003c/span\u003e are the initial distance and the corresponding capacitance between the resonant beam and electrode, respectively, \u003cspan\u003e\u003cspan\u003e\\({V}_{dc}\\)\u003c/span\u003e\u003c/span\u003e is the bias voltage applied on the resonant beam, \u003cspan\u003e\u003cspan\u003e\\({V}_{ac},{\\omega }_{d}\\)\u003c/span\u003e\u003c/span\u003e are the amplitude and angular frequency of the driven signal for the resonant beam.\u003c/p\u003e\n\u003cp\u003eAccording to our previous work\u003csup\u003e36\u003c/sup\u003e, a specifically designed resonant beam exhibits hybrid nonlinear dynamics including the duffing nonlinearity and the intrinsic transient exponential nonlinear response characteristics when it is seen as a typical underdamped second-order oscillation system, which guarantees the dynamic nonlinear features and fading memory of the reservoir. Thanks to the complex nonlinear phenomena caused by the scale effect and fabrication tolerance in the MEMS resonant accelerometers, the nonlinear dynamics of the resonant frequency and amplitude of the resonant beams with the external acceleration can act as a physical reservoir able to map temporal inputs into a feature space that can be analyzed by a trained readout layer. Figure \u003cspan\u003e2\u003c/span\u003ea shows the simulation result for the frequency shift (delta-f\u0026thinsp;=\u0026thinsp;f-f0) dependent dynamical nonlinearity of the resonant beam with the external acceleration input. Figure \u003cspan\u003e2\u003c/span\u003eb shows the simulation result for the amplitude dependent dynamical nonlinear hysteresis of the resonant beam with the external acceleration input, which is similar to the electrostatic spring softening effect in the duffing nonlinearity. As we all know, the hysteresis region between the two bifurcation points ([a=-54g, a=-1g]) reserves complex nonlinear dynamics. But as an edge sensor, the differential resonant accelerometer should be driven to an appropriate nonlinear region to ensure not only the nonlinear transformation of the input signal, but also the stable sensing of the external acceleration. Considering the resonant frequency of the resonant beam needs to be tracked and locked by a Phase Lock Loop (PLL), which is incompatible with the frequency detection through the closed-loop interface circuit. Therefore, we use the nonlinear response between the amplitude of the resonant beam and the external acceleration as the reservoir dynamics in this work. The grey region represents the optimal dynamic range of the input acceleration for our system, which corresponds to the classification accuracy over 90% for different motion postures, as shown in Fig. \u003cspan\u003e2\u003c/span\u003ed. Experimentally, we use electrostatic force instead of the external acceleration to perturbate the stiffness of the resonant beam to verify the dynamical nonlinearity of the device. The simulation and experimental results are shown in the Fig. \u003cspan\u003e2\u003c/span\u003ec.\u003c/p\u003e\n\u003cp\u003e.\u003c/p\u003e\n\u003cp\u003eThe experimental setup for the PRC with a stiffness modulated accelerometer\u003c/p\u003e\n\u003cp\u003eThe differential resonant accelerometer is packaged and integrated on a printed circuit board (PCB), which is driven by the electrostatic force instead of the external acceleration, and detected by an interface circuit, as shown in Fig. \u003cspan\u003e3\u003c/span\u003eb and \u003cstrong\u003ec\u003c/strong\u003e. To calibrate the external acceleration dependent electrostatic force, we fix the PCB with the packaged accelerometer on a triaxial rotating stage, and simulate the acceleration of \u0026plusmn;\u0026thinsp;1g by changing the orthogonal position between gravity and the sensitive axis, as shown in Fig. \u003cspan\u003e3\u003c/span\u003ea. A lock-in amplifier (Zurich Instruments MFLI500kHz/5MHz) is used to sweep frequency and detect the frequency shift. A power source (Keysight U8032A ) is used to apply electrostatic force to equilibrate the gravity. Results show that the electrostatic force corresponding to the 27.6V DC voltage is equal to the inertial force generated by 1g acceleration, as shown in Fig. \u003cspan\u003e2\u003c/span\u003ec. Figure \u003cspan\u003e3\u003c/span\u003ed shows the optical microscopy image of the differential resonant accelerometer with a scale bar of 1 mm. The comb driving structure, clamped-clamped beam structure, and micro lever structure are highlighted in red dotted frames 1, 2, 3, respectively, which correspond to the SEM images Fig. \u003cspan\u003e3\u003c/span\u003ee, Fig. \u003cspan\u003e3\u003c/span\u003ef, and Fig. \u003cspan\u003e3\u003c/span\u003eg.\u003c/p\u003e\n\u003cp\u003eThe classification for the acceleration input via the MEMS accelerometer-integrated RC\u003c/p\u003e\n\u003cp\u003eAs a novel physical reservoir without digital operation such as delay and mask, the designed resonant beam with hybrid nonlinear dynamics has shown excellent performance on feature extraction and classification based on some standard benchmarks\u003csup\u003e36\u003c/sup\u003e. In this work, we migrate this novel physical reservoir on the differential resonant accelerometer to make it an edge sensor. The priority is to verify its performance for the acceleration input corresponding to the different motion postures by the customized dataset acquired from a homemade six-axis IMU sensor, which is elaborated in our previous work\u003csup\u003e36\u003c/sup\u003e. Figure \u003cspan\u003e4\u003c/span\u003ea shows the different acceleration waveforms in the time domain corresponding to the 8 motion postures, including \u0026ldquo;Jump\u0026rdquo;, \u0026ldquo;Walk\u0026rdquo;, \u0026ldquo;Jog\u0026rdquo;, \u0026ldquo;Squat\u0026rdquo;, \u0026ldquo;Stretch\u0026rdquo;, \u0026ldquo;ChestE\u0026rdquo;, \u0026ldquo;ArmC\u0026rdquo;, and \u0026ldquo;BodyC. Thanks to the nonlinear dynamical mechanism that stiffness perturbation caused by the external acceleration and the non-delay architecture without mask operation in the digital domain, the input acceleration can be directly fed into the dynamics of the reservoir and be classified by feature extraction from the analog domain with low power consumption. Figure \u003cspan\u003e4\u003c/span\u003eb shows the color block diagram for the results of the different features corresponding to the 8 motion postures extracted by the nonlinear transformation of our MEMS accelerometer-integrated RC. We perform ten times tenfold cross-validation tests and use the confusion matrix to characterize the classification performance on the customized dataset for motion posture recognition. Each sample of the test dataset is divided into 15 groups and tested by ten times. Results show a classification accuracy of (97.33\u0026thinsp;\u0026plusmn;\u0026thinsp;0.136)%, as shown in Fig. \u003cspan\u003e4\u003c/span\u003ec. A box plot inset displays the discrete distribution of the data. Figure \u003cspan\u003e4\u003c/span\u003ed shows the results of the false-color confusion matrix. The color bar represents the number of samples whose predicted result are consistent with the target result. The power consumption of the core device including the accelerometer and its driving interface circuit in our prototype system is estimated to be less than 300\u0026thinsp;\u0026plusmn;\u0026thinsp;1mW, as shown in Fig. \u003cspan\u003e3\u003c/span\u003e. In our experimental setup, the power consumption of the interface circuit is approximated by Pc\u0026thinsp;=\u0026thinsp;5V\u0026times;0.06A\u0026thinsp;=\u0026thinsp;300mW, while the power consumption of the differential resonant accelerometer is approximated by Pa\u0026thinsp;=\u0026thinsp;100mV\u0026times;0.01A\u0026thinsp;+\u0026thinsp;10V\u0026times;0.01uA\u0026thinsp;=\u0026thinsp;1mW.\u003c/p\u003e\n"},{"header":"Discussion","content":"\u003cp\u003eMEMS resonant accelerometer exhibits rich nonlinear behaviors under large displacement oscillations, originating from the micro-scale effects, the intrinsic geometrical nonlinearity as well as the coupling effects of the multiple physical fields and so on. Although these nonlinearities limit the resolution and dynamic range for the acceleration measurement, they generate rich nonlinear dynamics required for the MEMS accelerometer-integrated RC, which makes it possible to efficiently process the temporal acceleration input that is sensed by the accelerometer. For instance, when the resonant beam is perturbed by a sufficiently large input acceleration through the proof mass and the micro lever structure connected to it, the accelerometer exhibits frequency-acceleration nonlinearity and the amplitude-acceleration nonlinearity. But the frequency-acceleration nonlinearity is not available because a fixed drive frequency is needed for the non-delayed PRC we proposed. Thus, we focus on the amplitude-acceleration nonlinearity as well as its intrinsic transient nonlinearity, and use this hybrid nonlinearity to implement the MEMS accelerometer-integrated RC. Besides, the mechanism that stiffness perturbation caused by the external acceleration allows the input acceleration to be directly fed into the dynamics of the reservoir and to be classified by feature extraction from the analog domain with low power consumption. Considering both of the two identical resonators of the differential resonant accelerometer possess the dual capabilities of sensing and computing, the sensing paradigm we proposed can provide more edge computing modes in future improvement. Except for the sensing mode or the reservoir computing mode, the differential resonant accelerometer can also realize the classification and recognition for a selected piece of acceleration input by applying the two resonators simultaneously, one serving as a threshold switch for acceleration signal monitoring and the other for information processing.\u003c/p\u003e \u003cp\u003eIn summary, we implement a novel sensing paradigm based on a novel non-delayed PRC structure we demonstrated previously using a stiffness modulated MEMS resonant accelerometer. and investigate the structure that converts the acceleration into axial tension to be added to the resonator dynamics. Furthermore, we investigate the nonlinear behavior of the MEMS resonant accelerometer and use the hybrid nonlinearity that is composed of amplitude-acceleration nonlinearity and transient nonlinearity to implement the non-delayed PRC. Moreover, we build a data set of the different accelerations corresponding to the different motion postures using a six-axis IMU to study the processing performance for the acceleration that causes the perturbation of the axial stiffness of the resonator dynamics. The results of the ten times tenfold cross-validation and the confusion matrix show a classification accuracy of 97.33%, which proves that our MEMS accelerometer-integrated RC enables data processing ability locally at the sensing side for efficient distributed processing. Additionally, these results also overcome the bottleneck of the traditional sensing paradigm relied on discrete sensors and physically separated processing units, where analog-to-digital conversion units between sensing and computing are indispensable, thus having the potential to improve the energy efficiency of information processing. This energy efficient method also facilitates the new future possibilities for exploring the emerging applications of the A2F in MEMS-based PRC.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eDevice fabrication details\u003c/p\u003e \u003cp\u003eThe MEMS differential resonant accelerometer is fabricated using the silicon micro-manufacture technology based on the standard Silicon on Insulator (SOI) micromachining process and multilayer silicon wafer bonding process. The fabrication process starts with a 6-inch SOI wafer (device thickness of 50\u0026micro;m, oxide thickness of 1\u0026micro;m, the substrate thickness of 380\u0026micro;m) with a pre-etched shallow trench. The bottom electrodes are defined by the patterned silicon that is isolated from each other by etching to expose the buried oxide (BOX) layer. Followed by the silicon-to-silicon bonding process to bond the second SOI wafer upside down to the predefined silicon electrodes after depositing the bond-plane silicon dioxide. Then remove the BOX layer and the substrate silicon of the second SOI, and define the top silicon electrodes by deep reactive ion etching (DRIE). Finally, bond a cap silicon wafer with etched cavities and deposit getter material to the aforementioned bond-plane silicon dioxide using the glass frit wafer bonding to achieve wafer-level hermetic packaging\u003c/p\u003e \u003cp\u003eDevice structure details\u003c/p\u003e \u003cp\u003eThe schematic illustration of the MEMS differential resonant accelerometer is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(C). Two identical resonant beams are connected to the suspended proof mass by micro-levers to amplify the acceleration induced inertial force. The thickness of the resonant beam and the suspended proof mass is 50\u0026micro;m, which depends on the device layer thickness of the SOI wafer. The suspended proof mass is about 4.269\u0026times;10^(-6) kg. The length and width of the resonant beam are designed based on the appropriate resonant frequency and quality factor for the MEMS accelerometer-integrated RC obtained by finite element simulation and the limitation of the fabrication. The length of the resonant beam is 400 \u0026micro;m, and the width of the resonant beam is 6 \u0026micro;m\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eContributions\u003c/p\u003e\n\u003cp\u003eAll authors participated in the scientific discussion. W.Y., J.S., and X.Z. conceived the idea. J.S. and W.Y. carried out most of the experiments, and W.Y. wrote the manuscript. W.Y. and J.S. equally contributed to this work. X.Z. and W.Y. provided the know-how and the concept of the proposed sensing paradigm of analog-to-feature (A2F). X.G. helped in the simulation and the measurement. X.G., X.X and Z.W analyzed the nonlinear behavior. X.X and Z.W helped in the design and the fabrication for the MEMS resonant accelerometer. Z.L and X.B attended the discussion and all authors participated in the revision of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements (optional)\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors would like to thank the members of the State Key Laboratory of Transducer Technology for helpful discussions.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThis research was partially supported by National Key Research and Development Program of China under Grant No. 2023YFB3207901,\u0026nbsp;the National Natural Science Foundation of China (Grant No. 61971399), and the Key Research Program of Frontier Science (CAS, Grant No. ZDBS-LY-JSC028).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics declarations\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCompeting\u0026nbsp;interests\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eKhoshnoud, F., de Silva, C. 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Non-linear frequency noise modulation in a resonant MEMS accelerometer. \u003cstrong\u003e17\u003c/strong\u003e, 4122-4127 (2017).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4343664/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4343664/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe current boom in Micro-electromechanical Systems combined with the advent of the physical reservoir computing make it possible to break through the bottleneck of traditional sensing paradigms based on physically separated sensors and processors. Here, we report a pioneering work on a novel sensing paradigm of analog-to-feature using a stiffness modulated micromechanical resonant accelerometer. Specifically, the amplitude-acceleration nonlinearity of the accelerometer and its transient nonlinearity serve as the nonlinear dynamics of our physical reservoir computing to categorize the accelerometer input. Furthermore, we perform ten times tenfold cross-validation tests and use the confusion matrix to test its classification performance on a data set of the different acceleration corresponding to the different motion postures generated by a six-axis IMU. The results show a classification accuracy of 97.33%, which proves that our MEMS accelerometer-integrated reservoir computing enables data processing ability locally at the sensing side for efficient distributed processing.\u003c/p\u003e","manuscriptTitle":"A sensing paradigm of analog-to-feature (A2F) based on the MEMS accelerometer-integrated reservoir computing","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-11 07:19:23","doi":"10.21203/rs.3.rs-4343664/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"51f9ad75-ad0f-45b2-9419-8ea5f0d3f37e","owner":[],"postedDate":"June 11th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-07-04T11:21:42+00:00","versionOfRecord":[],"versionCreatedAt":"2024-06-11 07:19:23","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4343664","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4343664","identity":"rs-4343664","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}