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Song H, Li Y, Zou X, Hu P, Liu T. Elite male table tennis matches diagnosis using SHAP and a hybrid LSTM-BPNN algorithm. Sci Rep 2023; 13:11533. [PMID: 37460573 DOI: 10.1038/s41598-023-37746-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2023] [Accepted: 06/27/2023] [Indexed: 07/20/2023] Open
Abstract
This study adopts a new approach, SHapley Additive exPlanation (SHAP), to diagnose the table tennis matches based on a hybrid algorithm, namely Long Short-Term Memory-Back Propagation Neural Network (LSTM-BPNN). 100 male singles competitions (8535 rallies) from 2019 to 2022 are analyzed by a hybrid technical-tactical analysis theory, which hybridizes the double three-phase and four-phase evaluation theories. A k-means cluster analysis is conducted to classify 59 players' winning rates into three levels (high, medium, and low). The results show that LSTM-BPNN has excellent performance (MSE = 0.000355, MAE = 0.014237, RMSE = 0.018853, and [Formula: see text] = 0.988311) compared with six typical artificial intelligence algorithms. Using LSTM-BPNN to calculate the SHAP value of each feature, the global results find that the receive-attack and serve-attack phases of the ending match have essential impacts on the mutual winning probabilities. Finally, case applications show that the SHAP can directly obtain each feature importance on one or more matches, which is more objective and reliable than the traditional simulation method. This research explores an innovative way to understand and analyze matches, and these results have implications for the performance analysis of table tennis and related racket sports.
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Affiliation(s)
- Honglin Song
- College of Physical Education and Sports, Beijing Normal University, Beijing, 100084, China
| | - Yutao Li
- College of Physical Education and Sports, Beijing Normal University, Beijing, 100084, China
| | - Xiaofeng Zou
- School of Physical Education, Jilin University, Jilin, 130015, China
| | - Ping Hu
- Microsoft, Beijing, 100080, China
| | - Tianbiao Liu
- College of Physical Education and Sports, Beijing Normal University, Beijing, 100084, China.
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Artificial Intelligence Technologies and Their Application for Reform and Development of Table Tennis Training in Complex Environments. COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2022; 2022:3442610. [PMID: 35747715 PMCID: PMC9213137 DOI: 10.1155/2022/3442610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Revised: 03/25/2022] [Accepted: 04/04/2022] [Indexed: 11/17/2022]
Abstract
The development of information technology has been deployed in almost all sectors and is making life easier. In this development, the sports sector has seen tremendous expansion. In traditional table tennis training, the coach and the players have to meet daily to take appropriate training for the game. This process is time-consuming in a complex environment, and it will have a significant impact on the reformation and development of table tennis training. The utilization of improved technologies can overcome this challenge by performing training of the game online with an intelligent wireless system with advanced training mechanisms. Carrying the traditional and heavier intelligent wireless devices will be difficult for the players. In this research, the fine-grained evaluation (FGE) system is incorporated into the deep learning model to analyze the player's body postures during the training and event sessions and make them develop after each session through online training in any circumstance. The proposed FGE was compared with the traditional statistical model, and it was observed that the proposed FGE had obtained higher precision and recall values of 70% and 98.9% than the statistical model.
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Huang X, Sharma A, Shabaz M. Biomechanical research for running motion based on dynamic analysis of human multi-rigid body model. INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2022. [DOI: 10.1007/s13198-021-01563-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
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Measuring Upper Limb Kinematics of Forehand and Backhand Topspin Drives with IMU Sensors in Wheelchair and Able-Bodied Table Tennis Players. SENSORS 2021; 21:s21248303. [PMID: 34960397 PMCID: PMC8706454 DOI: 10.3390/s21248303] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Revised: 12/08/2021] [Accepted: 12/09/2021] [Indexed: 11/17/2022]
Abstract
To better understand the biomechanics of para-table tennis players, this study compared the shoulder, elbow, and wrist joint kinematics among able-bodied (AB) and wheelchair players in different classifications. Nineteen participants (AB, n = 9; classification 1 (C1), n = 3; C2, n = 3; C3, n = 4) executed 10 forehand and backhand topspin drives. Shoulder abduction/adduction, elbow flexion/extension, wrist extension/flexion, respective range of motion (ROM), and joint patterns were obtained using inertial measurement unit (IMU) sensors. The results showed clear differences in upper limb kinematics between the able-bodied and wheelchair players, especially in the elbow and wrist. For the para-players, noticeable variations in techniques were also observed among the different disability classes. In conclusion, wheelchair players likely adopted distinct movement strategies compared to AB to compensate for their physical impairments and functional limitations. Hence, traditional table tennis programs targeting skills and techniques for able-bodied players are unsuitable for para-players. Future work can investigate how best to customize training programs and to optimize movement strategies for para-players with varied types and degrees of impairment.
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Kholkine L, Servotte T, de Leeuw AW, De Schepper T, Hellinckx P, Verdonck T, Latré S. A Learn-to-Rank Approach for Predicting Road Cycling Race Outcomes. Front Sports Act Living 2021; 3:714107. [PMID: 34693282 PMCID: PMC8527032 DOI: 10.3389/fspor.2021.714107] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2021] [Accepted: 08/19/2021] [Indexed: 11/18/2022] Open
Abstract
Professional road cycling is a very competitive sport, and many factors influence the outcome of the race. These factors can be internal (e.g., psychological preparedness, physiological profile of the rider, and the preparedness or fitness of the rider) or external (e.g., the weather or strategy of the team) to the rider, or even completely unpredictable (e.g., crashes or mechanical failure). This variety makes perfectly predicting the outcome of a certain race an impossible task and the sport even more interesting. Nonetheless, before each race, journalists, ex-pro cyclists, websites and cycling fans try to predict the possible top 3, 5, or 10 riders. In this article, we use easily accessible data on road cycling from the past 20 years and the Machine Learning technique Learn-to-Rank (LtR) to predict the top 10 contenders for 1-day road cycling races. We accomplish this by mapping a relevancy weight to the finishing place in the first 10 positions. We assess the performance of this approach on 2018, 2019, and 2021 editions of six spring classic 1-day races. In the end, we compare the output of the framework with a mass fan prediction on the Normalized Discounted Cumulative Gain (NDCG) metric and the number of correct top 10 guesses. We found that our model, on average, has slightly higher performance on both metrics than the mass fan prediction. We also analyze which variables of our model have the most influence on the prediction of each race. This approach can give interesting insights to fans before a race but can also be helpful to sports coaches to predict how a rider might perform compared to other riders outside of the team.
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Affiliation(s)
- Leonid Kholkine
- Department of Computer Science, University of Antwerp-IMEC, Antwerp, Belgium
| | - Thomas Servotte
- Department of Mathematics, University of Antwerp, Antwerp, Belgium
| | | | - Tom De Schepper
- Department of Computer Science, University of Antwerp-IMEC, Antwerp, Belgium
| | - Peter Hellinckx
- Department of Computer Science, University of Antwerp-IMEC, Antwerp, Belgium
| | - Tim Verdonck
- Department of Mathematics, University of Antwerp, Antwerp, Belgium
| | - Steven Latré
- Department of Computer Science, University of Antwerp-IMEC, Antwerp, Belgium
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Creating a Scoring System with an Armband Wearable Device for Table Tennis Forehand Loop Training: Combined Use of the Principal Component Analysis and Artificial Neural Network. SENSORS 2021; 21:s21113870. [PMID: 34205215 PMCID: PMC8200036 DOI: 10.3390/s21113870] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/26/2021] [Revised: 05/28/2021] [Accepted: 06/01/2021] [Indexed: 11/17/2022]
Abstract
BACKGROUND This study presents an intelligent table tennis e-training system based on a neural network (NN) model that recognizes data from sensors built into an armband device, with the component values (performances scores) estimated through principal component analysis (PCA). METHODS Six expert male table tennis players on the National Youth Team (mean age 17.8 ± 1.2 years) and seven novice male players (mean age 20.5 ± 1.5 years) with less than 1 year of experience were recruited into the study. Three-axis peak forearm angular velocity, acceleration, and eight-channel integrated electromyographic data were used to classify both player level and stroke phase. Data were preprocessed through PCA extraction from forehand loop signals. The model was trained using 160 datasets from five experts and five novices and validated using 48 new datasets from one expert and two novices. RESULTS The overall model's recognition accuracy was 89.84%, and its prediction accuracies for testing and new data were 93.75% and 85.42%, respectively. Principal components corresponding to the skills "explosive force of the forearm" and "wrist muscle control" were extracted, and their factor scores were standardized (0-100) to score the skills of the players. Assessment results indicated that expert scores generally fell between 60 and 100, whereas novice scores were less than 70. CONCLUSION The developed system can provide useful information to quantify expert-novice differences in fore-hand loop skills.
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Table Tennis Tutor: Forehand Strokes Classification Based on Multimodal Data and Neural Networks. SENSORS 2021; 21:s21093121. [PMID: 33946262 PMCID: PMC8124603 DOI: 10.3390/s21093121] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/26/2021] [Revised: 04/22/2021] [Accepted: 04/27/2021] [Indexed: 12/03/2022]
Abstract
Beginner table-tennis players require constant real-time feedback while learning the fundamental techniques. However, due to various constraints such as the mentor’s inability to be around all the time, expensive sensors and equipment for sports training, beginners are unable to get the immediate real-time feedback they need during training. Sensors have been widely used to train beginners and novices for various skills development, including psychomotor skills. Sensors enable the collection of multimodal data which can be utilised with machine learning to classify training mistakes, give feedback, and further improve the learning outcomes. In this paper, we introduce the Table Tennis Tutor (T3), a multi-sensor system consisting of a smartphone device with its built-in sensors for collecting motion data and a Microsoft Kinect for tracking body position. We focused on the forehand stroke mistake detection. We collected a dataset recording an experienced table tennis player performing 260 short forehand strokes (correct) and mimicking 250 long forehand strokes (mistake). We analysed and annotated the multimodal data for training a recurrent neural network that classifies correct and incorrect strokes. To investigate the accuracy level of the aforementioned sensors, three combinations were validated in this study: smartphone sensors only, the Kinect only, and both devices combined. The results of the study show that smartphone sensors alone perform sub-par than the Kinect, but similar with better precision together with the Kinect. To further strengthen T3’s potential for training, an expert interview session was held virtually with a table tennis coach to investigate the coach’s perception of having a real-time feedback system to assist beginners during training sessions. The outcome of the interview shows positive expectations and provided more inputs that can be beneficial for the future implementations of the T3.
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A Deep Learning Approach for Table Tennis Forehand Stroke Evaluation System Using an IMU Sensor. COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2021; 2021:5584756. [PMID: 33868398 PMCID: PMC8033526 DOI: 10.1155/2021/5584756] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/16/2021] [Revised: 03/05/2021] [Accepted: 03/19/2021] [Indexed: 11/17/2022]
Abstract
Psychological and behavioral evidence suggests that home sports activity reduces negative moods and anxiety during lockdown days of COVID-19. Low-cost, nonintrusive, and privacy-preserving smart virtual-coach Table Tennis training assistance could help to stay active and healthy at home. In this paper, a study was performed to develop a Forehand stroke' performance evaluation system as the second principal component of the virtual-coach Table Tennis shadow-play training system. This study was conducted to show the effectiveness of the proposed LSTM model, compared with 2DCNN and RBF-SVR time-series analysis and machine learning methods, in evaluating the Table Tennis Forehand shadow-play sensory data provided by the authors. The data was generated, comprising 16 players' Forehand strokes racket's movement and orientation measurements; besides, the strokes' evaluation scores were assigned by the three coaches. The authors investigated the ML models' behaviors changed by the hyperparameters values. The experimental results of the weighted average of RMSE revealed that the modified LSTM models achieved 33.79% and 4.24% estimation error lower than 2DCNN and RBF-SVR, respectively. However, the R ¯ 2 results show that all nonlinear regression models are fit enough on the observed data. The modified LSTM is the most powerful regression method among all the three Forehand types in the current study.
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Chatterjee A, Gerdes M, Prinz A, Martinez S. Human Coaching Methodologies for Automatic Electronic Coaching (eCoaching) as Behavioral Interventions With Information and Communication Technology: Systematic Review. J Med Internet Res 2021; 23:e23533. [PMID: 33759793 PMCID: PMC8074867 DOI: 10.2196/23533] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2020] [Revised: 12/28/2020] [Accepted: 02/15/2021] [Indexed: 01/17/2023] Open
Abstract
BACKGROUND We systematically reviewed the literature on human coaching to identify different coaching processes as behavioral interventions and methods within those processes. We then reviewed how those identified coaching processes and the used methods can be utilized to improve an electronic coaching (eCoaching) process for the promotion of a healthy lifestyle with the support of information and communication technology (ICT). OBJECTIVE This study aimed to identify coaching and eCoaching processes as behavioral interventions and the methods behind these processes. Here, we mainly looked at processes (and corresponding models that describe coaching as certain processes) and the methods that were used within the different processes. Several methods will be part of multiple processes. Certain processes (or the corresponding models) will be applicable for both human coaching and eCoaching. METHODS We performed a systematic literature review to search the scientific databases EBSCOhost, Scopus, ACM, Nature, SpringerLink, IEEE Xplore, MDPI, Google Scholar, and PubMed for publications that included personal coaching (from 2000 to 2019) and persuasive eCoaching as behavioral interventions for a healthy lifestyle (from 2014 to 2019). The PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) framework was used for the evidence-based systematic review and meta-analysis. RESULTS The systematic search resulted in 79 publications, including 72 papers and seven books. Of these, 53 were related to behavioral interventions by eCoaching and the remaining 26 were related to human coaching. The most utilized persuasive eCoaching methods were personalization (n=19), interaction and cocreation (n=17), technology adoption for behavior change (n= 17), goal setting and evaluation (n=16), persuasion (n=15), automation (n=14), and lifestyle change (n=14). The most relevant methods for human coaching were behavior (n=23), methodology (n=10), psychology (n=9), and mentoring (n=6). Here, "n" signifies the total number of articles where the respective method was identified. In this study, we focused on different coaching methods to understand the psychology, behavioral science, coaching philosophy, and essential coaching processes for effective coaching. We have discussed how we can integrate the obtained knowledge into the eCoaching process for healthy lifestyle management using ICT. We identified that knowledge, coaching skills, observation, interaction, ethics, trust, efficacy study, coaching experience, pragmatism, intervention, goal setting, and evaluation of coaching processes are relevant for eCoaching. CONCLUSIONS This systematic literature review selected processes, associated methods, strengths, and limitations for behavioral interventions from established coaching models. The identified methods of coaching point toward integrating human psychology in eCoaching to develop effective intervention plans for healthy lifestyle management and overcome the existing limitations of human coaching.
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Affiliation(s)
- Ayan Chatterjee
- Department for Information and Communication Technologies, Centre for e-Health, University of Agder, Grimstad, Norway
| | - Martin Gerdes
- Department for Information and Communication Technologies, Centre for e-Health, University of Agder, Grimstad, Norway
| | - Andreas Prinz
- Department for Information and Communication Technologies, Centre for e-Health, University of Agder, Grimstad, Norway
| | - Santiago Martinez
- Department of Health and Nursing Science, Centre for e-Health, University of Agder, Grimstad, Norway
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Ishac K, Eager D. Evaluating Martial Arts Punching Kinematics Using a Vision and Inertial Sensing System. SENSORS 2021; 21:s21061948. [PMID: 33802201 PMCID: PMC8001023 DOI: 10.3390/s21061948] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/12/2021] [Revised: 02/26/2021] [Accepted: 03/06/2021] [Indexed: 11/16/2022]
Abstract
Martial arts has many benefits not only in self-defence, but also in improving physical fitness and mental well-being. In our research we focused on analyzing the velocity, impulse, momentum and impact force of the Taekwondo sine-wave punch and reverse-step punch. We evaluated these techniques in comparison with the martial arts styles of Hapkido and Shaolin Wushu and investigated the kinematic properties. We developed a sensing system which is composed of an ICSensor Model 3140 accelerometer attached to a punching bag for measuring dynamic acceleration, Kinovea motion analysis software and 2 GoPro Hero 3 cameras, one focused on the practitioner's motion and the other focused on the punching bag's motion. Our results verified that the motion vectors associated with a Taekwondo practitioner performing a sine-wave punch, uses a unique gravitational potential energy to optimise the impact force of the punch. We demonstrated that the sine-wave punch on average produced an impact force of 6884 N which was higher than the reverse-step punch that produced an average impact force of 5055 N. Our comparison experiment showed that the Taekwondo sine-wave punch produced the highest impact force compared to a Hapkido right cross punch and a Shaolin Wushu right cross, however the Wushu right cross had the highest force to weight ratio at 82:1. The experiments were conducted with high ranking black belt practitioners in Taekwondo, Hapkido and Shaolin Wushu.
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Sport Biomechanics Applications Using Inertial, Force, and EMG Sensors: A Literature Overview. Appl Bionics Biomech 2020; 2020:2041549. [PMID: 32676126 PMCID: PMC7330631 DOI: 10.1155/2020/2041549] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2019] [Revised: 05/26/2020] [Accepted: 06/05/2020] [Indexed: 11/17/2022] Open
Abstract
In the last few decades, a number of technological developments have advanced the spread of wearable sensors for the assessment of human motion. These sensors have been also developed to assess athletes' performance, providing useful guidelines for coaching, as well as for injury prevention. The data from these sensors provides key performance outcomes as well as more detailed kinematic, kinetic, and electromyographic data that provides insight into how the performance was obtained. From this perspective, inertial sensors, force sensors, and electromyography appear to be the most appropriate wearable sensors to use. Several studies were conducted to verify the feasibility of using wearable sensors for sport applications by using both commercially available and customized sensors. The present study seeks to provide an overview of sport biomechanics applications found from recent literature using wearable sensors, highlighting some information related to the used sensors and analysis methods. From the literature review results, it appears that inertial sensors are the most widespread sensors for assessing athletes' performance; however, there still exist applications for force sensors and electromyography in this context. The main sport assessed in the studies was running, even though the range of sports examined was quite high. The provided overview can be useful for researchers, athletes, and coaches to understand the technologies currently available for sport performance assessment.
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A Systematic Literature Review of Intelligent Data Analysis Methods for Smart Sport Training. APPLIED SCIENCES-BASEL 2020. [DOI: 10.3390/app10093013] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
The rapid transformation of our communities and our way of life due to modern technologies has impacted sports as well. Artificial intelligence, computational intelligence, data mining, the Internet of Things (IoT), and machine learning have had a profound effect on the way we do things. These technologies have brought changes to the way we watch, play, compete, and also train sports. What was once simply training is now a combination of smart IoT sensors, cameras, algorithms, and systems just to achieve a new peak: The optimum one. This paper provides a systematic literature review of smart sport training, presenting 109 identified studies. Intelligent data analysis methods are presented, which are currently used in the field of Smart Sport Training (SST). Sport domains in which SST is already used are presented, and phases of training are identified, together with the maturity of SST methods. Finally, future directions of research are proposed in the emerging field of SST.
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Uddin M, Syed-Abdul S. Data Analytics and Applications of the Wearable Sensors in Healthcare: An Overview. SENSORS 2020; 20:s20051379. [PMID: 32138291 PMCID: PMC7085778 DOI: 10.3390/s20051379] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 02/26/2020] [Accepted: 02/29/2020] [Indexed: 12/11/2022]
Affiliation(s)
- Mohy Uddin
- Executive Office, King Abdullah International Medical Research Center, King Saud bin Abdulaziz University for Health Sciences, King Abdulaziz Medical City, Ministry of National Guard—Health Affairs, Riyadh 11426, Saudi Arabia;
| | - Shabbir Syed-Abdul
- Graduate Institute of Biomedical Informatics, Taipei Medical University, Taipei 10675, Taiwan
- Correspondence: ; Tel.: +886-2-6638-2736 (ext. 1514); Fax: +886-2-6638-0233
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Silva MC, Amorim VJP, Ribeiro SP, Oliveira RAR. Field Research Cooperative Wearable Systems: Challenges in Requirements, Design and Validation. SENSORS (BASEL, SWITZERLAND) 2019; 19:E4417. [PMID: 31614802 PMCID: PMC6832741 DOI: 10.3390/s19204417] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/30/2019] [Revised: 10/06/2019] [Accepted: 10/08/2019] [Indexed: 12/13/2022]
Abstract
The widespread availability of wearable devices is evolving them into cooperative systems. Communication and distribution aspects such as the Internet of Things, Wireless Body Area Networks, and Local Wireless Networks provide the means to develop multi-device platforms. Nevertheless, the field research environment presents a specific feature set, which increases the difficulty in the adoption of this technology. In this text, we review the main aspects of Field Research Gears and Wearable Devices. This review is made aiming to understand how to create cooperative systems based on wearable devices directed to the Field Research Context. For a better understanding, we developed a case study in which we propose a cooperative system architecture and provide validation aspects. For this matter, we provide an overview of a previous device architecture and study an integration proposal.
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Affiliation(s)
- Mateus C Silva
- Department of Computing, Federal University of Ouro Preto, Morro do Cruzeiro Campus, Ouro Preto 35400-000, Brazil.
| | - Vicente J P Amorim
- Department of Computing, Federal University of Ouro Preto, Morro do Cruzeiro Campus, Ouro Preto 35400-000, Brazil.
| | - Sérvio P Ribeiro
- Department of Biology, Federal University of Ouro Preto, Morro do Cruzeiro Campus, Ouro Preto 35400-000, Brazil.
| | - Ricardo A R Oliveira
- Department of Computing, Federal University of Ouro Preto, Morro do Cruzeiro Campus, Ouro Preto 35400-000, Brazil.
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