Extended Gaussian mixture regression for forward and inverse analysis

Soft sensor model development in multiphase/multimode processes based on Gaussian mixture regression

ABSTRACTWe present a comprehensive teleoperation framework for electric vehicle (EV) battery cell handling, integrating haptic feedback, extended reality (XR) visualization, and task‐parameterized Gaussian mixture regression (TP‐GMR) for adaptive, real‐time trajectory generation. The system enables seamless switching between manual and autonomous operation through a variable autonomy mechanism, while constraint barrier functions (CBFs) enforce spatial safety constraints. A lightweight intent prediction module anticipates user deviation and precomputes corrective trajectories, reducing response time from 2.0 s to under 1 ms. The framework is implemented on an industrial KUKA robotic manipulator and validated in structured and real‐world EV battery disassembly scenarios. Results show that combining XR and haptic feedback reduces task completion time by up to 48% and path deviation by 32%, compared to manual teleoperation without assistance. Predictive replanning improves continuity of force feedback and reduces unnecessary user motion. The integration of XR‐based spatial computing, learning‐from‐demonstration, and real‐time control enables safe, precise, and efficient manipulation in high‐risk environments. This study demonstrates a scalable human‐in‐the‐loop solution for battery recycling and other semi‐structured tasks, where full automation is impractical. The proposed system significantly improves operator performance while maintaining safety and flexibility, marking a meaningful advancement in collaborative field robotics.

Mixture of regression model is widely used to cluster subjects from a suspected heterogeneous population due to differential relationships between response and covariates over unobserved subpopulations. In such applications, statistical evidence pertaining to the significance of a hypothesis is important yet missing to substantiate the findings. In this case, one may wish to test hypotheses regarding the effect of a covariate such as its overall significance. If confirmed, a further test of whether its effects are different in different subpopulations might be performed. This paper is motivated by the analysis of Chiroptera dataset, in which, we are interested in knowing how forearm length development of bat species is influenced by precipitation within their habitats and living regions using finite Gaussian mixture regression (GMR) model. Since precipitation may have different effects on the evolutionary development of the forearm across the underlying subpopulations among bat species worldwide, we propose several testing procedures for hypotheses regarding the effect of precipitation on forearm length under finite GMR models. In addition to the real analysis of Chiroptera data, through simulation studies, we examine the performances of these testing procedures on their type I error rate, power, and consequently, the accuracy of clustering analysis.

Particulate matter air pollution is a leading cause of global mortality, particularly in Asia and Africa. Addressing the high and wide-ranging air pollution levels requires ambient monitoring, but many low- and middle-income countries (LMICs) remain scarcely monitored. To address these data gaps, recent studies have utilized low-cost sensors. These sensors have varied performance, and little literature exists about sensor intercomparison in Africa. By colocating 2 QuantAQ Modulair-PM, 2 PurpleAir PA-II SD, and 16 Clarity Node-S Generation II monitors with a reference-grade Teledyne monitor in Accra, Ghana, we present the first intercomparisons of different brands of low-cost sensors in Africa, demonstrating that each type of low-cost sensor PM2.5 is strongly correlated with reference PM2.5, but biased high for ambient mixture of sources found in Accra. When compared to a reference monitor, the QuantAQ Modulair-PM has the lowest mean absolute error at 3.04 μg/m3, followed by PurpleAir PA-II (4.54 μg/m3) and Clarity Node-S (13.68 μg/m3). We also compare the usage of 4 statistical or machine learning models (Multiple Linear Regression, Random Forest, Gaussian Mixture Regression, and XGBoost) to correct low-cost sensors data, and find that XGBoost performs the best in testing (R2: 0.97, 0.94, 0.96; mean absolute error: 0.56, 0.80, and 0.68 μg/m3 for PurpleAir PA-II, Clarity Node-S, and Modulair-PM, respectively), but tree-based models do not perform well when correcting data outside the range of the colocation training. Therefore, we used Gaussian Mixture Regression to correct data from the network of 17 Clarity Node-S monitors deployed around Accra, Ghana, from 2018 to 2021. We find that the network daily average PM2.5 concentration in Accra is 23.4 μg/m3, which is 1.6 times the World Health Organization Daily PM2.5 guideline of 15 μg/m3. While this level is lower than those seen in some larger African cities (such as Kinshasa, Democratic Republic of the Congo), mitigation strategies should be developed soon to prevent further impairment to air quality as Accra, and Ghana as a whole, rapidly grow.

Learning from demonstration (LfD), which provides a natural way to transfer skills to robots, has been extensively researched for decades, and an army of methods and applications have been developed and investigated for learning an individual or low-level task. Nevertheless, learning long time sequential tasks is still very difficult as it involves task segmentation and sub-task clustering under an extremely large demonstration variance. Besides, the representation problem should be considered when doing segmentation. This paper presents a new unified framework to solve the problems of segmentation, clustering, and representation in a sequential task. The segmentation algorithm segments unstructured demonstrations into movement primitives (MPs). Then, the MPs are automatically clustered and labeled so that they can be reused in other tasks. Finally, the representation model is leveraged to encode and generalize the learned MPs in new contexts. To achieve the first goal, a change-point detection algorithm based on Bayesian inference is leveraged. It can segment unstructured demonstrations online with minimum prior knowledge requirements. By following the Gaussian distributed assumption in the segmentation model, MPs are encoded by Gaussians or Gaussian mixture models. Thus, the clustering of MPs is formulated as a clustering over cluster (CoC) problem. The Kullback–Leibler divergence is used to measure similarities between MPs, through which the MPs with smaller distance are clustered into the same group. To replay and generalize the task in novel contexts, we use task-parameterized regression models such as the Gaussian mixture regression. We implemented our framework on a sequential open-and-place task. The experiments demonstrate that the segmentation accuracy of our framework can reach 94.3% and the recognition accuracy can reach 97.1%. Comparisons with the state-of-the-art algorithm also indicate that our framework is superior or comparable to their results.

Cable-driven rehabilitation robots can be used to recover the upper-limb motor function of hemiplegia patients after stroke. In this study, a statistical approach was proposed to enable a 3-DOF upper-limb cable-driven rehabilitation robot (UCDRR) to predict the human intention by learning human skills from demonstrations. Specifically, in the learning phase, Gaussian mixture model (GMM) was exploited to statistically analyze the human-robot interaction features (i.e., Electromyography (EMG) and interaction force) based on the recorded demonstrator-robot interaction data. Then, during prediction, the robot estimated the interaction force from the measured EMG by using Gaussian mixture regression (GMR). The experimental results of the interaction force prediction in simulation demonstrated that the proposed approach could statistically extract the variable information from the multiple demonstrations successfully and estimate subject-robot interaction forces with high accuracy. This study will help the UCDRR to provide assistance as needed to hemiplegia patients during rehabilitation training, thereby promoting the active participation.

Impedance control allows robots to manipulate physical interactions delicately. However, issues associated with path planning and impedance remain unresolved. Herein we propose a path and impedance planning method for impedance control in a robot based on programming by demonstration through telemanipulation using a surface electromyogram. We considered a task that requires quick and precise adjustment of path and impedance, that is, ball trapping. We implemented a teleoperated robot that can deliver an operator's impedance as well as position during the ball trapping task to the slave side. The operators were asked to perform demonstrations of ball-trapping tasks using the implemented teleoperated robot, where the slave side is a vertical robot with one degree of freedom. The path and impedance were recorded and programmed as control input profiles from a set of successful demonstrations using Gaussian mixture regression. The result showed that using the human demonstration, the robot could learn how to catch a dropped ball without rebounding.

Wearable motion sensing in daily life has attracted attention in various disciplines. Especially, stretchable strain sensors have been instrumented into garments (e.g. brace). To estimate joint motions from such sensors, previous studies have modelled relationships between the sensor strains and motion parameters via supervised/semi-supervised learning. However, typically these only model a single relationship assuming the sensor to be located at a specific point on the body. Consequently, they exhibit reduced performance when the strain-parameter relationship varies due to sensor shifts caused by long-term wearing or donning/doffing of braces. This letter presents a shift-adaptive estimation of knee joint angle. First, a brace is instrumented with two stretch sensors placed at different heights. Next, the different strain-angle relationships at varying brace shift positions are learned using Gaussian mixture models (GMMs). The system then estimates the joint angle from the sensor strains through Gaussian mixture regression using a maximum likelihood shift GMM, which is identified by referring to the two strains in a previous 1 s period. Experimental results indicated that the proposed method estimates the joint angle at multiple shift positions (0-20 mm) with higher accuracy than methods using a single model, single sensor, or referring to the present sensor strains.

Prognostics and health management (PHM) is one of the research hotspots in reliability, where remaining useful life (RUL) estimation is a typical application scenario. In this article, a feature learning method based on dynamic Bayesian networks (DBNs) is proposed to improve the RUL estimation accuracy of the regression models. The best feature set is obtained with the conditional dependencies represented by the DBN structure. A local modeling method is applied here to reduce the computation for high-order DBN construction. The strength of the connections between variables together with a contribution index of variables in the DBN structure are defined to represent the feature importance of the variables. Feature transfer is carried out with feature importance under different operating conditions for a further improvement. Nonlinear regression models such as support vector regression (SVR) and Gaussian mixture regression (GMR) are built based on the learned features and used to estimate the RUL. The turbofan engine dataset C-MAPSS is used to validate the effectiveness of the proposed method. Compared with other recent RUL estimation models, the proposed method has a faster modeling speed and higher prediction accuracy.

This paper presents a novel force learning framework to learn fingertip force for a grasping and manipulation process from a human teacher with a force imaging approach. A demonstration station is designed to measure fingertip force without attaching force sensor on fingertips or objects so that this approach can be used with daily living objects. A Gaussian Mixture Model (GMM) based machine learning approach is applied on the fingertip force and position to obtain the motion and force model. Then a force and motion trajectory is generated with Gaussian Mixture Regression (GMR) from the learning result. The force and motion trajectory is applied to a robotic arm and hand to carry out a grasping and manipulation task. An experiment was designed and carried out to verify the learning framework by teaching a Fanuc robotic arm and a BarrettHand a pick-and-place task with demonstration. Experimental results show that the robot applied proper motions and forces in the pick-and-place task from the learned model.

This paper presents the design and application of the SAFER glove in the field of hand rehabilitation. The authors present preliminary results on a new hand grasping rehabilitation learning system that is designed to gather kinematic and force information of the human hand and to playback the motion to assist a user in common hand grasping movements, such as grasping a bottle of water. The fingertip contact forces during grasping have been measured by the SAFER Glove from 12 subjects. The measured fingertip contact forces were modeled with Gaussian Mixture Model (GMM) based on machine learning approach. The learned force distributions were then used to generate fingertip force trajectories with a Gaussian Mixture Regression (GMR) method. To demonstrate the glove’s potential to manipulate the hand, experiments with the glove fitted on a wooden hand to grasp various objects were performed. Instead of defining a grasping force, contact force trajectories were used to control the SAFER Glove to actuate/assist this hand while carrying out a learned grasping task. To prove that the hand can be driven safely by the haptic mechanism, force sensor readings placed between each finger and the mechanism have been plotted. The experimental results show the potential of the proposed system in future hand rehabilitation therapy.

We focus on assisting mobile robot teleoperation in a task-appropriate way, where we model the user intention as an action primitive to perform a contextual task, e.g. doorway crossing and object inspection, and provide motion assistance according to the task recognition. This paper contributes to formulating motion assistance in a data-driven manner. With the motion clusters obtained in our previous report [1], we apply a fast online Gaussian Mixture Regression (GMR) approach to the most probable motion cluster classified during operation, to estimate the local trajectory the human user intends to follow in the short term for the corresponding task execution with the recognized contextual information. To regulate the estimation accuracy, we compute the Mahalanobis distance of each estimated trajectory way point. By thresholding the distance, we can achieve the trajectory estimation within a pre-defined tolerance bound regarding the regression outliers. The experimental results from both the qualitative and quantitative tests using the real data confirmed the effectiveness and real-time performance of the proposed approach.

In recent years, with the widespread application of shortwave infrared (SWIR) spectroscopy in mineral identification and hydrothermal alteration studies, an increasing number of studies have attempted to integrate SWIR spectral data with machine learning approaches to fully exploit mineralization-related discriminative information embedded in high-dimensional spectral datasets. In this study, the Zhunuo porphyry copper deposit in Tibet was selected as the research target. SWIR drill core spectral data were systematically acquired, and a random forest (RF) machine learning model was applied to full-band SWIR spectra (1300–2500 nm) to conduct integrated analyses of copper grade regression and mineralization discrimination. A total of 2140 drill core samples were measured, with three replicate measurements per sample, yielding 6420 spectra. After standardized preprocessing and interpolation resampling, a unified spectral feature dataset was constructed for regression and classification analyses. SWIR spectral data are characterized by a large number of bands, strong inter-band correlations, and relatively limited sample sizes; under such conditions, model generalization ability and stability become critical factors in method selection. Based on ensemble learning, the random forest model constructs multiple decision trees and aggregates their predictions through voting or averaging, effectively reducing model variance and mitigating overfitting, and is therefore well suited for high-dimensional, small-sample, and highly correlated geological spectral datasets. In porphyry copper systems, the spectral characteristics of hydrothermal alteration minerals and mineralization intensity commonly exhibit complex nonlinear relationships, which can be effectively captured by random forest models without requiring predefined functional forms. The regression results indicate that accurate quantitative prediction of copper grade based solely on SWIR spectral data remains limited. In contrast, when a threshold-based binary classification was introduced using an industrial cutoff grade of 0.2% Cu, the model achieved an overall accuracy of 75%, an F1 score of 0.69, and an area under the ROC curve (AUC) of 0.80, demonstrating strong mineralization discrimination capability and stability. Overall, the integration of SWIR spectroscopy with machine learning methods provides an efficient, reliable, and geologically interpretable technical approach for early-stage exploration and detailed drill core interpretation in porphyry copper deposits.

Deep drawing process is an important process adding values to flat sheet metals in many industries. An important concern in the design of a deep drawing process generally is formability. This paper aims to present the connection between formability and inverse analysis (IA), which is a systematical means for determining an optimal blank configuration for a deep drawing process. In this paper, IA is presented and explored by using a commercial finite element software package. A number of numerical studies on the effect of blank configurations to the quality of a part produced by a deep drawing process were conducted and analyzed. The quality of the drawing processes is numerically analyzed by using an explicit incremental nonlinear finite element code. The minimum distance between elemental principal strains and the strain-based forming limit curve (FLC) is defined as tearing margin to be the key performance index (KPI) implying the quality of the part. The initial blank configuration has shown that it plays a highly important role in the quality of the product via the deep drawing process. In addition, it is observed that if a blank configuration is not greatly deviated from the one obtained from IA, the blank can still result a good product. The strain history around the bottom fillet of the part is also observed. The paper concludes that IA is an important part of the design methodology for deep drawing processes.

There are several uses for biomass-derived materials (BDMs) in the irrigation and farming industries. To solve problems with material, process, and supply chain design, BDM systems have started to use machine learning (ML), a new technique approach. This study examined articles published since 2015 to understand better the current status, future possibilities, and capabilities of ML in supporting environmentally friendly development and BDM applications. Previous ML applications were classified into three categories according to their objectives: material and process design, performance prediction and sustainability evaluation. ML helps optimize BDMs systems, predict material properties and performance, reverse engineering, and solve data difficulties in sustainability evaluations. Ensemble models and cutting-edge Neural Networks operate satisfactorily on these datasets and are easily generalized. Ensemble and neural network models have poor interpretability, and there have not been any studies in sustainability assessment that consider geo-temporal dynamics; thus, building ML methods for BDM systems is currently not practical. Future ML research for BDM systems should follow a workflow. Investigating the potential uses of ML in BDM system optimization, evaluation and sustainable development requires further investigation.