Real-time human activity recognition (HAR) is crucial for adaptive control in lower limb exoskeletons, yet achieving an optimal balance between accuracy, latency, and sensor complexity remains challenging. This study's key idea is to systematically evaluate sensor selection and data modalities for real-time HAR using deep neural networks with ultra-short 50 ms sliding windows. Leveraging a dataset from 21 subjects performing six locomotion activities and employing three deep learning models (MLP, LSTM, CNN-LSTM), we assess multiple sensor combinations, including joint angle data, derived angular velocities, and inertial measurements, and quantify their trade-offs across accuracy, latency, and model complexity. Our analysis reveals that bilateral joint angles from hip, knee, and ankle achieve 98.98% accuracy, significantly outperforming unilateral sensor setups. Adding a thigh-mounted IMU further elevates accuracy to 99.23%, highlighting the advantages of multimodal sensor fusion. Additionally, incorporating derived joint angular velocities enhances accuracy, with up to 15% increase when using single-joint bilateral inverse kinematics data. Even a minimal configuration, such as bilateral hip joints with derived angular velocities, achieves over 94% accuracy, offering practical solutions for low-power wearable systems. These findings establish actionable design principles for HAR-driven control in assistive robotics and mobile health applications.

Monitoring the metabolic rate of occupational workers who often perform physically demanding tasks is of significance in maintaining their performance and safety. We investigate the viability of accurate metabolic rate estimation from heart rate measurements in physically demanding occupational activities, with data collected from simulated firefighter activities. Various regression methods including linear regression, tree-based methods, kernel-based methods, support vector machine (SVM), and neural networks are employed to predict breath-by-breath metabolic rates for firefighting activities under three different loading conditions: firefighting gear, gear + self-contained breathing apparatus (SCBA), and gear + SCBA + 10 lb. With both heart rate and activity types as predictors, the best-performing machine learning method (Coarse Gaussian SVM) is able to estimate metabolic rate with R2= 0.90 and RMSE = 0.375 for activities under the two SCBA conditions, and the method is robust against differences in the subjects’ heart rates and metabolic rates from cross-validation. Without activity types as predictors, the prediction accuracy is significantly lower (decreases by 34% on average). Future research to incorporate IMU sensors and/or force insoles as additional predictors for metabolic rate could eliminate the reliance on activity types, thus enhancing the generality and applicability of the method for a broader range of occupational and daily activities.

Differential equations are fundamental in modeling numerous physical systems, including thermal, manufacturing, and meteorological systems. Traditionally, numerical methods often approximate the solutions of complex systems modeled by differential equations. With the advent of modern deep learning, Physics-informed Neural Networks (PINNs) are evolving as a new paradigm for solving differential equations with a pseudo-closed form solution. Unlike numerical methods, the PINNs can solve the differential equations mesh-free, integrate the experimental data, and resolve challenging inverse problems. However, one of the limitations of PINNs is the poor training caused by using the activation functions designed typically for purely data-driven problems. This work proposes a scalable tanh-based activation function for PINNs to improve learning the solutions of differential equations. The proposed Self-scalable tanh (Stan) function is smooth, non-saturating, and has a trainable parameter. It can allow an easy flow of gradients and enable systematic scaling of the input-output mapping during training. Various forward problems to solve differential equations and inverse problems to find the parameters of differential equations demonstrate that the Stan activation function can achieve better training and more accurate predictions than the existing activation functions for PINN in the literature.

Background/foreground separation is one of the most fundamental tasks in computer vision, especially for video data. Robust PCA (RPCA) and its tensor extension, namely, Robust Tensor PCA (RTPCA), provide an effective framework for background/foreground separation by decomposing the data into low-rank and sparse components, which contain the background and the foreground (moving objects), respectively. However, in real-world applications, the video data is contaminated with noise. For example, in metal additive manufacturing (AM), the processed X-ray video to study melt pool dynamics is very noisy. RPCA and RTPCA are not able to separate the background, foreground, and noise simultaneously. As a result, the noise will contaminate the background or the foreground or both. There is a need to remove the noise from the background and foreground. To achieve the three components decomposition, a smooth sparse Robust Tensor Decomposition (SS-RTD) model is proposed to decompose the data into static background, smooth foreground, and noise, respectively. Specifically, the static background is modeled by the low-rank tucker decomposition, the smooth foreground (moving objects) is modeled by the spatio-temporal continuity, which is enforced by the total variation regularization, and the noise is modeled by the sparsity, which is enforced by the$\ell _{1}$norm. An efficient algorithm based on alternating direction method of multipliers (ADMM) is implemented to solve the proposed model. Extensive experiments on both simulated and real data demonstrate that the proposed method significantly outperforms the state-of-the-art approaches for background/foreground separation in noisy cases. Note to Practitioners—This work is motivated by melt pool detection in metal additive manufacturing where the processed X-ray video from the monitoring system is very noisy. The objective is to recover the background with porosity defects and the foreground with melt pool in the presence of noise. Existing methods fail to separate the noise from the background and foreground since RPCA and RTPCA have only two components, which cannot explain the three components in the data. This paper puts forward a smooth sparse Robust Tensor Decomposition by decomposing the tensor data into low-rank, smooth, and sparse components, respectively. It is a highly effective method for background/foreground separation in noisy case. In the case studies on simulated video and X-ray data, the proposed method can handle non-additive noise, and even the case of high noise-ratio. In the proposed algorithm, there is only one tuning parameter$\lambda $. Based on the case studies, our method achieves satisfying performance by taking any$\lambda \in [{0.2,1}]$with anisotropic total variation regularization. With this observation, practitioners can apply the proposed method without extensive parameter tuning work. Furthermore, the proposed method is also applicable to other popular industrial applications. Practitioners can use the proposed SS-RTD for degradation processes monitoring, where the degradation image contains the static background, anomaly, and random disturbance, respectively.

Robust PCA (RPCA) and its tensor extension, namely, Robust Tensor PCA (RTPCA), provide an effective framework for background/foreground separation by decomposing the data into low-rank and sparse components, which contain the background and the foreground (moving objects), respectively. However, in real-world applications, the presence of missing pixels is a very common and challenging issue due to errors in the acquisition process or manufacturer defects. RPCA and RTPCA are not able to recover the background and foreground simultaneously with missing pixels. This study aims to address the problem of background/foreground separation with missing pixels by combining video recovery and background/foreground separation into a single framework. To achieve this goal, a smooth robust tensor completion (SRTC) model is proposed to recover the data and decompose it into the static background and smooth foreground, respectively. An efficient algorithm based on tensor proximal alternating minimization (tenPAM) is implemented to solve the proposed model with a global convergence guarantee under very mild conditions. Extensive experiments on actual data demonstrate that the proposed method significantly outperforms the state-of-the-art approaches for background/foreground separation with missing pixels.

The recent increase in applications of high-dimensional data poses a severe challenge to data analytics, such as supervised classification, particularly for online applications. To tackle this challenge, efficient and effective methods for feature extraction are critical to the performance of classification analysis. The objective of this work is to develop a new supervised feature extraction method for high-dimensional data. It is achieved by developing a clustered discriminant regression (CDR) to extract informative and discriminant features for high-dimensional data. In CDR, the variables are clustered into different groups or subspaces, within which feature extraction is performed separately. The CDR algorithm, which is a greedy approach, is implemented to obtain the solution toward optimal feature extraction. One numerical study is performed to demonstrate the performance of the proposed method for variable selection. Three case studies using healthcare and additive manufacturing data sets are accomplished to demonstrate the classification performance of the proposed methods for real-world applications. The results clearly show that the proposed method is superior over the existing method for high-dimensional data feature extraction.Note to Practitioners—This article forwards a new supervised feature extraction method termed clustered discriminant regression. This method is highly effective for classification analysis of high-dimensional data, such as images or videos, where the number of variables is much larger than the number of samples. In our case studies on healthcare and additive manufacturing, the performance of classification analysis based on our method is superior over the existing feature extraction methods, which is confirmed by using various popular classification algorithms. For image classification, our method with elaborately selected classification algorithms can outperform a convolutional neural network. In addition, the computation efficiency of the proposed method is also promising, which enables its online applications, such as advanced manufacturing process monitoring and control.