Physics-Constrained Deep Learning Model for Contactless Blood Pressure Monitoring from Triaxial Bodyseismography

Yuanyuan Zhang; Yida Zhang; Jiahui Li; Yuyan Wu; Fei Dou; Xiao Yin; Zhenlin An; Hae Young Noh

eess.SPAug 24, 2026

Physics-Constrained Deep Learning Model for Contactless Blood Pressure Monitoring from Triaxial Bodyseismography

Authors: Yuanyuan Zhang, Yida Zhang, Jiahui Li, Yuyan Wu, Fei Dou, Xiao Yin, Zhenlin An, Hae Young Noh, +1 more

Organizations: School of Electrical and Computer Engineering, University of Georgia, Athens, 30603, United States · School of Computing, University of Georgia, Athens, 30603, United States · Department of Civil and Environmental Engineering, Stanford University, Stanford, CA, 94305, United States · Yixing People’s Hospital, Wuxi 214200, China

Abstract

Ballistocardiography (BCG) is promising for unobtrusive long-term blood pressure (BP) monitoring in laboratory settings, but traditional BCG signals are vulnerable to the variations in body-bed interaction with shifted fiducial points in temporal or amplitude axis, and BP varies with personal hemodynamic changes, causing misaligned representations that affect model generalizability and robustness. In this work, we propose Phy-BP, a physics-constrained BP estimation framework based on triaxial bodyseismography (BSG) acquired using bed-mounted sensors as an extension of single-axis BCG. Firstly, we design an adaptive quality-control algorithm combining neighboring beat patterns and universal cardiogenic templates to retain reliable cardiac components. Secondly, we propose a physical model of wave propagation through the body-bed system to constrain latent feature evolution, aligning triaxial representations generated by a shared cardiogenic excitation. These mechanical constraints connect multi-axis feature learning to body-bed dynamics and complement data-driven regression from vibration signals. Evaluation on a 162-hour hospital dataset from 21 subjects against invasive arterial BP yields a mean absolute error of 5.07 mmHg, a prediction-error standard deviation of 7.24 mmHg, and a Pearson correlation coefficient of 0.86 for mean arterial pressure. This framework is intended for unobtrusive monitoring during rest and sleep, with potential applications in overnight hospital and home monitoring.

Figures & tables

Fig. 1: Illustration of BSG sensors placement and signals under similar systolic blood pressure (SBP) and diastolic blood pressure (DBP): (a) Standard BSG signal with the majority of features shown in Y-axis; (b) Energy leakage to X-axis with no observable features in Y-axis; (c) Distorted BSG signal due to soft/thick mattress with attenuated and shifted fiducial peaks.

Fig. 2: Correspondence between fiducial points and cardiac events as summarized in [ 33 , 18 , 19 ] .

Fig. 3: Overview of Phy-BP: (a) Quality control based on Y-axis BSG to retain signals rich in cardiogenic components; (b) Physical model that governs wave propagation excited by heartbeat; (c) Deep learning model designed with the triaxial feature extraction aligned and constrained by the physical model.

Fig. 4: Design of matched filters with cardiogenic and dynamic templates.

Panel of Figure 5 — Fig. 5: Signal-level assessment of the reduced model: (a) Measured signals and fitting results; (b) Overall fitting Pearson correlation coefficient (PCC); (c) Modal frequency distributions.

Encoder Layers	Parameters	Output Shape
Encoder Layers	( $C_{in}$ , $C_{out}$ , $K$ , $S$ ) 1	$N$ : Batch Size
Input signal	–	$(N,2,1000)$
Encoder
Conv1d	$(2,64,7,2)$	$(N,64,500)$
MaxPool	$(64,64,3,2)$	$(N,64,250)$
Residual Block $\times 2$	$(64,16,3,1)$	$(N,16,250)$

TABLE I: Structure and Parameters for the Encoder and Decoder

Fig. 6: Design of physics-constrained layer: (a) Gate-based feature alignment to aggregate triaxial features; (b) Physics-constrained regularization to govern the feature evolution during network training.

Panel of Figure 8 — Fig. 7: Overview of the dataset: (a) Data collection overview; (b) MAP Distribution; (c) MAP by Age, with the numerical annotations indicating BMI.

Panel of Figure 9 — Fig. 8: Performance overview of Phy-BP (Full) with different colors for different subjects: (a) - (c) Bland-Altman plot for SBP, DBP and MAP; (d) - (f) Correlation plot for SBP, DBP and MAP.

Panel of Figure 10 — Fig. 9: Subject-level BP estimation performance in terms of MAE and STD.

Panel of Figure 11 — Fig. 10: MAP prediction error across subjects: (a) MAE of MAP prediction; (b) and (c) Association between TPR variability and MAP prediction error before and after adjustment for MAP RMSSD, respectively.

Fig. 11: Overall performance versus computational complexity, with marker sizes representing parameter counts.

Panel of Figure 13 — Fig. 12: Training Phy-BP using different scales of data: (a) - (c) MAE, STD and PCC changes for the model with or without the physics constraint (PC); (d) Overall degradation in terms of SBP, DBP and MAP.

Panel of Figure 14 — Fig. 13: Effectiveness of the quality control with different thresholds for required matched cardiac cycles.

Panel of Figure 15 — Fig. 14: Effectiveness and coverage after quality control: (a) - (c) The performance of BP prediction in terms of MAE, STD and PCC, respectively; (d) - (e) Sample-wise retention and minute coverage with different quality-control thresholds.

Settings for	SBP				DBP				MAP				Overall
Phy-BP	MAE $\downarrow$	ME $\to$ 0	STD $\downarrow$	PCC $\uparrow$	MAE $\downarrow$	ME $\to$ 0	STD $\downarrow$	PCC $\uparrow$	MAE $\downarrow$	ME $\to$ 0	STD $\downarrow$	PCC $\uparrow$	$\Delta m\%\uparrow$
	Using Different Input Axes
Y only	$10.64$	$5.19$	$15.63$	$0.41$	$6.65$	$0.99$	$7.71$	$0.44$	$6.28$	$1.86$	$8.79$	$0.65$	$-13.80\%$
Z only	$10.28$	$-1.20$	$11.96$	$0.70$	$5.58$	$-0.27$	$8.62$	$0.72$	$7.11$	$-1.59$	$10.41$	$0.73$	$-0.54\%$
X+Y	$6.32$	$-1.14$	$7.23$	$0.78$	$5.12$	$0.22$	$7.16$	$0.72$	$6.79$	$0.13$	$9.78$	$0.76$	$16.12\%$
X+Z	$8.37$	$-1.66$	$10.03$	$0.68$	$6.32$	$0.85$	$8.39$	$0.61$	$6.40$	$0.59$	$11.63$	$0.62$	$-0.78\%$

TABLE III: Ablation studies under different settings

Yuanyuan Zhang is currently a Postdoctoral Associate with the SensorWeb Laboratory at the University of Georgia, Athens, GA, USA. He received the Ph.D. and B.Eng. degrees in Electrical and Electronic Engineering from the University of Liverpool, UK, in 2025 and 2020, respectively, and the M.S. degree in Control Systems from Imperial College London, UK, in 2021. His current research interests include wireless sensing, bioradar systems, bodyseismography, blood pressure monitoring, and physiological digital twins.

Table 17

Yida Zhang is currently pursuing the Ph.D. degree in Electrical and Computer Engineering at the University of Georgia. He received his bachelor’s degree in Computer Science and Technology from Hohai University, Nanjing, China, in 2024. His current research interests include mobile computing, human sensing, and physiological signal processing.

Table 18

Jiahui Li is a Ph.D. student in Computer Science at the University of Georgia. His research interests include mobile and wearable sensing, human-centered AI, and healthcare applications.

Table 19

Yuyan Wu is a Ph.D. candidate in Civil and Environmental Engineering at Stanford University. She received her B.S. degree in Applied Physics, with a minor in Computer Science, from the University of Science and Technology of China. Her research focuses on indirect human and animal monitoring through ambient vibration sensing.

Table 20

Fei Dou is an Assistant Professor in the School of Computing at the University of Georgia. She received her Ph.D. in Computer Science and Engineering from the University of Connecticut in 2023. Her research interests include machine learning, ubiquitous computing, intelligent sensing, and AI for health. Fei is the recipient of the Women of Innovation (WOI) Academic Innovation and Leadership Award in Connecticut.

Table 21

Xiao Yin is currently pursuing the Ph.D. degree in Electronic Information at the School of Electronic Science and Engineering, Nanjing University, Nanjing, China. He is also an Attending Physician with the Department of Critical Care Medicine, Yixing People’s Hospital, Yixing, China.

Table 22

Zhenlin An received the B.E. degree from the School of Information and Communication Engineering, Dalian University of Technology, China, in 2017, and the Ph.D. degree from the Department of Computing, The Hong Kong Polytechnic University, in 2021. He was a postdoctoral fellow with Princeton University and the University of Pittsburgh. He is currently an Assistant Professor with the School of Computing, University of Georgia. His research interests include wireless communication, indoor localization, and mobile computing.

Table 23

Hae Young Noh is a Professor in Civil and Environmental Engineering (CEE) at Stanford University. She received her Ph.D. and M.S. degrees in CEE and EE from Stanford, and her B.S. degree in Mechanical & Aerospace Engineering from Cornell. Her research focuses on indirect-sensing and physics-guided data analytics using “structures as sensors” to enable scalable, non-intrusive monitoring of cyber-physical-human systems.

Table 24

WenZhan Song (Senior Member, IEEE) received the B.S. and M.S. degrees in computer science from Nanjing University of Science and Technology, Nanjing, China, in 1997 and 1999, respectively, and the Ph.D. degree in computer science from Illinois Institute of Technology, Chicago, IL, USA, in 2005. He is currently the Chair Professor of electrical and computer engineering at the University of Georgia, Athens, GA, USA. He is also the founder of Intelligent Dots LLC, Peachtree Corners, GA, USA. His laboratory invented a series of noninvasive sensing technologies for the health and security monitoring of humans, animals, machines, and infrastructure, driven by the convergence of AI, data science, and advanced sensing and networking technologies. His research focuses on sensor data analytics and security, sensor networks, and data infrastructures.

Table 25

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Cuffless Blood Pressure Estimation Remote Photoplethysmography Electrocardiography Stress

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Continuous cuffless blood pressure (BP) monitoring remains challenging due to motion artifacts, physiological variability, and the limited robustness of conventional pulse transit time (PTT) models under dynamic conditions. Many prior approaches rely on multi-second windows to stabilize estimation, an assumption that is frequently violated during real-world monitoring with intermittent signal corruption. Here, we show that discriminative BP-related information is preserved at the single-beat level and present a lightweight multi-modal wearable framework for continuous BP estimation. The system integrates synchronized chest electrocardiography (ECG) and ear-clip reflectance photoplethysmography, each co-located with a 6-axis inertial measurement unit to provide motion context. We introduce a hybrid learning architecture in which a one-dimensional convolutional neural network extracts a 64-dimensional embedding from individual PPG beats and fuses it with 30 physiology-grounded features, including PTT statistics and heart rate variability, followed by LightGBM regression. The method was evaluated using a multi-phase stress protocol (

n=10

) and the PulseDB public dataset with subject-disjoint validation. Across 30 independent runs, the model achieved mean absolute errors of

4.02 \pm 0.21

~mmHg for systolic BP and

1.79 \pm 0.05

~mmHg for diastolic BP, corresponding to a 28.2% reduction in combined MAE relative to baseline models. By enabling beat-wise estimation without long temporal context, this framework supports computationally efficient cuffless BP monitoring suitable for wearable deployment under practical resource constraints. The source code for this work is available at https://github.com/SYMBIOX-Lab/BP-wireless.

Abstract

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