In-sensor human gait analysis with machine learning in a wearable microfabricated accelerometer

The study addresses how to tightly couple sensing and computation within a single physical device to enable efficient, private, and robust machine learning at the edge. In-sensor computing processes physical stimuli in the same domain as sensing, avoiding conventional transduction to electronics and separate digital processing. Mechanical computing elements (e.g., MEMS switches and resonators) offer compact, low-power operation and are naturally compatible with sensors of mechanical quantities such as acceleration. The authors hypothesize that a MEMS accelerometer whose mechanical degrees of freedom are harnessed via reservoir computing can perform real-time classification of human gait patterns using a single wearable device, with improved energy efficiency and built-in data privacy compared to conventional sensor-plus-microcontroller systems. They further posit that such a system can be robust to variability in human gait, walking speed, morphology, and non-ideal sensor characteristics, demonstrating a viable path for edge and wearable applications.

The paper situates the work within mechanical and in-sensor computing. Prior research has developed mechanical computing primitives (memory, logic) using micro- and nano-resonators and switches, envisioned for low-power edge applications. In-sensor computing has been explored with devices that directly process physical stimuli to yield classification or control outputs, including acoustic-resonator speech recognition, shape-identifying metamaterials, and in-materio computing. Physical reservoir computing provides a framework to exploit nonlinear dynamical systems for machine learning; examples include optoelectronic, spintronic, and memristive reservoirs with in-sensor capabilities (e.g., RF-to-spin reservoirs, light-sensitive memristor RC). Within MEMS, several works used nonlinear resonators and coupled structures for reservoir computing and action recognition, but comprehensive wearable, real-time in-sensor gait classification with energy and privacy considerations remained to be demonstrated.

Device and in-sensor computing architecture: A custom MEMS accelerometer integrates sensing and computation by coupling a suspended inertial proof mass to a doubly clamped silicon beam resonator that exhibits nonlinear (Duffing-type) dynamics. External accelerations (0.5–15 Hz, ~1 g) displace the proof mass, modulating the electrostatic drive amplitude applied to the beam at ~250 kHz; due to the quadratic force–voltage relation, the beam oscillates in-plane near ~500 kHz with a decay time ~150 µs. The beam’s oscillation envelope is a complex nonlinear function of the proof mass displacement (hence acceleration), forming the physical reservoir. To increase dimensionality and effective memory, a delayed feedback loop and time-multiplexing create N=100 virtual nodes. The envelope is sampled faster than the beam decay (sampling period << 150 µs); activations are produced at 14,285 Hz, linearly combined with trained weights to yield raw classification signals, then smoothed by a moving average over 300 timesteps to match the biomechanics timescale (~2.1 s effective). Thresholding yields binary detectors for toe-out (TO) and trunk-lean (TL), enabling four-class outputs: N, TO, TL, TOTL. MEMS design and packaging: Fabricated on SOI (50 µm device layer, 4 µm BOX released by HF vapor etch), with a proof mass (~49 µg in ~1 mm²) suspended by folded flexures (spring constant ~6.8 N/m) to ensure uniaxial sensitivity and limit transverse/rotational motion. The beam is 4 µm wide, 300 µm long, separated from the mass by an 8 µm electrostatic gap. Piezoresistive strain gauges (1.5 µm × 12 µm) provide differential readout; stoppers (18 µm half-discs) limit proof mass motion to 5 µm. The die is wire-bonded to a 20×20 mm PCB carrier, enclosed and shielded; the control electronics board integrates high-voltage drive with amplitude modulation, analog front-end, ADC/DAC, microcontroller, delayed feedback, leaky integrator, output linear layer, wireless/data logging (non-essential for inference in final design). Gait protocol: Ten healthy adults (age 33 ± 15 y; height 173 ± 8 cm; weight 75 ± 13 kg) walked on a treadmill with the MEMS device attached to the left shoe and a co-located reference accelerometer (Analog Devices ADXL326). Speeds: 0.36, 0.45, 0.54, 0.63, 0.72 m/s; for each, participants performed four 90 s sequences (after discarding first 10 s) in patterns N, TO, TL, TOTL, with supervision to ensure correctness. Signals were sampled at 14,285 Hz (downsampled appropriately for reference). Cables were secured to minimize interference. Training and inference: Virtual node activations x(n) are produced by leaky integration of digitized beam envelope samples: x(n) = (1−α) x(n−1) + α x̃(n), with N=100 nodes per timestep n. After discarding an initial transient (1000 timesteps), activations are arranged in X ∈ R^{(1+N)×M} (with bias row). Targets Y ∈ R^{2×M} encode TO and TL as one-hot; classes map to [0,0] (N), [1,0] (TO), [0,1] (TL), [1,1] (TOTL). Output weights W_out ∈ R^{2×(1+N)} are obtained by ridge regression: W_out = Y X^T (X X^T + β I)^{-1}. During inference, y(n) = W_out x(n) is temporally averaged (window 300) and thresholded (threshold chosen to minimize |TPR−TNR| per detector) to produce binary TO/TL detections and 4-class labels. Hyperparameters (e.g., leak α, feedback delay, gains) were tuned empirically. Evaluation: Personalized classifiers per participant via 4-fold cross-validation: for each split, train on 3 folds, test on 1; report average ROC AUC across splits. Real-time on-device classification was tested by transferring trained weights to the wearable system; demonstration video provided. Baselines: (1) Echo State Network (ESN) using single-channel acceleration input from the commercial accelerometer with N equal to the MEMS virtual nodes, tanh reservoir, CHARC-optimized key hyperparameters (input/bias scaling, spectral radius, leak); trained with ridge regression and identical post-processing. (2) Logistic Regression (LR) using a 5 s window of filtered acceleration (FIR Hamming, 71.5 Hz cutoff, order 40), features of 358 downsampled points plus mean, standardized; trained with liblinear (C=1.0). Both baselines used the same 4-fold protocol and 300-sample moving average. Power measurement and projections: Power was measured in inference (no data transmission) using a 5 V bench supply and ammeter. The MEMS prototype (including non-essential subsystems) consumed 970 ± 10 mW (calculated 958 mW by subsystem summation using measured signal characteristics, load impedances, device quiescent currents, and regulator efficiencies). A conventional system (ESP32-based Feather + ISM330DHCX IMU) running the ESN consumed 280 ± 40 mW. Projections for an optimized MEMS system (remove non-essential circuits, consolidate to single 2.5 V rail, lower-power components, replace multiplier with digital potentiometer-based amplitude control, remove logging) yield 94 mW; co-integration and vacuum packaging to raise Q could reduce below 12 mW. Further reductions possible by eliminating electronic feedback, creating activations entirely mechanically (e.g., multiple resonators/proof masses), and performing the linear combination in analog with adaptable elements (e.g., memristor arrays).

- Real-time, on-foot, in-sensor gait classification: The MEMS device, integrating sensing and reservoir computing in the mechanical domain, successfully discriminated between N, TO, TL, and TOTL gait patterns using a single accelerometer on the left shoe. - High detection performance: Representative ROC operating points showed TO detector TPR > 99% with FPR < 1%; TL detector around TPR ≈ 90% with FPR ≈ 10% in real-time tests for a single subject. - Cross-validated AUC across subjects/speeds: When using a single set of weights across all walking speeds for all participants, median AUC was 90% (TO) and 84% (TL); performance degradation primarily occurred between N vs TO and TL vs TOTL confusions. - Superiority to linear classifier: Logistic regression performed near chance on TL across participants/speeds (median AUC ~56%), and was inferior to the MEMS device on TO when combining speeds, demonstrating the need for nonlinear processing. - Parity with software ESN: The MEMS in-sensor classifier achieved classification performance comparable to a software ESN using a commercial accelerometer, despite the MEMS sensor’s non-idealities, indicating effective learning of both task variability and sensor nonlinearities. - Energy measurements and projections: Prototype MEMS system power was 970 ± 10 mW (calculated 958 mW), similar in scale to a heavily optimized microcontroller ESN system at 280 ± 40 mW. Simple redesigns project MEMS power at 94 mW; more advanced integration could reduce below 12 mW, indicating substantial efficiency advantages for highly integrated in-sensor devices. - Privacy by design: Only classification labels are wirelessly transmitted; raw accelerations are nonlinearly transformed within the MEMS before digitization and cannot be feasibly inverted, providing built-in data security and reduced transmission load.

The work demonstrates that co-integrating sensing and computation within a MEMS accelerometer enables robust, nonlinear time-series classification of human gait using a single wearable device, addressing the challenge of coupling sensor and computational degrees of freedom. By exploiting the nonlinear dynamics of a doubly clamped beam modulated by an inertial mass, and augmenting with delayed feedback and time-multiplexing, the device provides sufficient dimensionality and memory to handle realistic variability in gait signals. Comparable accuracy to a software ESN baseline confirms that the physical reservoir effectively processes biomechanical signals despite non-ideal sensor characteristics, while outperforming linear methods highlights the necessity of nonlinear computation for this task. The system’s architecture naturally limits data exposure to high-level labels and reduces bandwidth demands, aligning with privacy and energy constraints in wearables and IoT. Power analysis further indicates that integrated in-sensor designs can surpass conventional separated sensor-processor systems in efficiency, especially with straightforward optimizations and deeper co-integration, reinforcing the relevance of in-sensor computing for edge deployments.

This study presents a complete wearable MEMS accelerometer that performs in-sensor neuromorphic computing to classify clinically relevant gait patterns in real time, demonstrating high accuracy (AUC up to ~0.90 for TO and ~0.84 for TL across subjects/speeds), resilience to inter-subject and speed variability, and intrinsic data privacy. Performance matches that of a software ESN baseline and surpasses a linear classifier, underscoring the value of nonlinear mechanical computation. Power measurements and subsystem analyses reveal a clear path to substantial efficiency gains—projected to ~94 mW with modest redesigns and potentially <12 mW with advanced integration—making the approach attractive for long-lived, small-form-factor wearables and IoT nodes. Future work should focus on: (i) eliminating or reducing electronic feedback by creating mechanical activations (e.g., multiple resonators/proof masses) to further cut power; (ii) implementing the linear output layer in the analog domain with adaptable elements (e.g., memristor arrays) to support on-device learning; (iii) co-integration and vacuum packaging to enhance Q and reduce drive/readout power; and (iv) expanding generalization across broader activities, environments, and populations.

- Sensor non-idealities: The prototype accelerometer exhibited modest sensitivity (0.05–0.1 V/g over 400 Hz), in-band resonances, and other issues; the classifier learned around these limitations, but improved sensor performance could enhance margins. - Personalization and generalization: Classifiers were personalized per participant; performance decreased when using a single weight set across all speeds, with confusions between N vs TO and TL vs TOTL, indicating limits to full generalization without adaptive or multi-condition training. - Power of prototype vs projections: The current device consumed ~970 mW due to non-essential subsystems and suboptimal components; efficiency claims rely on projected redesigns and deeper integration not yet implemented in the prototype. - Feedback electronics dependency: The approach currently depends on delayed electronic feedback and digital processing for activations and weighting; a fully mechanical or analog implementation with comparable memory (~seconds) and node count (~100) has not yet been shown. - Training on-device: Weight adjustment is performed off-line and transferred; mechanisms for efficient, reliable on-device learning (e.g., analog adaptive arrays) are proposed but not yet realized.