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Soft Sensors and Intelligent Algorithms for Data Fusion

A special issue of Sensors (ISSN 1424-8220). This special issue belongs to the section "Sensor Networks".

Deadline for manuscript submissions: closed (30 September 2017) | Viewed by 80547

Special Issue Editors


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Guest Editor
Department of Engineering, University of Messina, Contrada Di Dio, Vill. S. Agata , 98166 Messina, Italy
Interests: system identification; soft sensors; soft computing; machine learning; neural networks; nonlinear control; complex systems; industrial automation; process monitoring
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Laboratory of Telecommunications and Signal Processing, Department of Electrical and Electronic Engineering, University of West Attica, University Campus 1, Ag. Spyridonos Str., GR-12243 Egaleo, Athens, Greece
Interests: computational intelligence; evolutionary computation; intelligent control; neural networks; swarm intelligence
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Laboratory of Telecommunications and Signal Processing; Department of Electrical and Electronic Engineering; University of West Attica; University Campus 1; Ag. Spyridonos Str., GR-12243, Egaleo, Athens, Greece
Interests: biometrics; handwriting recognition; decision classifiers; embedded systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Over the past few years, Soft Sensors have been established as valuable tools for estimating the value of a physical quantity, without actually measuring it. Soft sensors present some remarkable advantages over traditional hardware-based sensors, not only improving the availability of measurements, but also increasing their accuracy and reliability, and reducing the associated cost and time delays. As soft sensors are usually data-driven, relying on data fusion to provide a mathematical model for the physical quantity to be estimated, their development is catalysed by recent advancements in scientific fields like machine learning and computational intelligence.

Soft sensor implementations cover a broad spectrum of fields, ranging from industrial applications, to non-destructive testing and multimodal biometrics. The aim of this Special Issue is to bring together innovative developments in soft sensors, including advancements in intelligent algorithms and data fusion techniques for soft sensor development, as well as succesfull soft sensor applications. Papers addressing the wide range of aspects of this technology are invited, including, but not limited to:

  • Computational intelligence methods for soft sensors design
  • Soft sensor learning algorithms
  • Semi-supervised learning for soft sensor design
  • Hard and soft sensor data fusion
  • Adaptive soft sensors
  • Feature selection in soft sensors
  • Industrial soft sensors
  • Soft sensors for inferential control
  • Soft sensors for monitoring and fault detection
  • Chemical soft sensors
  • Data fusion of implantable and/or wearable sensors
  • Multi-modal biometrics (including face, handwriting, fingerprint, gait, iris/retina, voice, typing rhythm, hand, etc.)
  • Soft sensors for environmental applications
  • Soft sensors for non-destructive testing
  • Soft sensors for social sensing
  • Soft sensors in medical applications
  • Soft sensors in the smart grid context

Prof. Maria Gabriella Xibilia
Dr. Alex Alexandridis
Dr. Elias N. Zois
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Sensors is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Computational intelligence
  • Data fusion
  • Fault detection
  • Inferential sensors
  • Machine learning
  • Multimodal biometrics
  • Non-destructive testing
  • Soft computing
  • Soft sensors
  • Virtual sensors

Published Papers (14 papers)

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Research

17 pages, 1402 KiB  
Article
On the Comparison of Wearable Sensor Data Fusion to a Single Sensor Machine Learning Technique in Fall Detection
by Panagiotis Tsinganos and Athanassios Skodras
Sensors 2018, 18(2), 592; https://doi.org/10.3390/s18020592 - 14 Feb 2018
Cited by 58 | Viewed by 6808
Abstract
In the context of the ageing global population, researchers and scientists have tried to find solutions to many challenges faced by older people. Falls, the leading cause of injury among elderly, are usually severe enough to require immediate medical attention; thus, their detection [...] Read more.
In the context of the ageing global population, researchers and scientists have tried to find solutions to many challenges faced by older people. Falls, the leading cause of injury among elderly, are usually severe enough to require immediate medical attention; thus, their detection is of primary importance. To this effect, many fall detection systems that utilize wearable and ambient sensors have been proposed. In this study, we compare three newly proposed data fusion schemes that have been applied in human activity recognition and fall detection. Furthermore, these algorithms are compared to our recent work regarding fall detection in which only one type of sensor is used. The results show that fusion algorithms differ in their performance, whereas a machine learning strategy should be preferred. In conclusion, the methods presented and the comparison of their performance provide useful insights into the problem of fall detection. Full article
(This article belongs to the Special Issue Soft Sensors and Intelligent Algorithms for Data Fusion)
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19 pages, 3381 KiB  
Article
An Inverse Neural Controller Based on the Applicability Domain of RBF Network Models
by Alex Alexandridis, Marios Stogiannos, Nikolaos Papaioannou, Elias Zois and Haralambos Sarimveis
Sensors 2018, 18(1), 315; https://doi.org/10.3390/s18010315 - 22 Jan 2018
Cited by 9 | Viewed by 5673
Abstract
This paper presents a novel methodology of generic nature for controlling nonlinear systems, using inverse radial basis function neural network models, which may combine diverse data originating from various sources. The algorithm starts by applying the particle swarm optimization-based non-symmetric variant of the [...] Read more.
This paper presents a novel methodology of generic nature for controlling nonlinear systems, using inverse radial basis function neural network models, which may combine diverse data originating from various sources. The algorithm starts by applying the particle swarm optimization-based non-symmetric variant of the fuzzy means (PSO-NSFM) algorithm so that an approximation of the inverse system dynamics is obtained. PSO-NSFM offers models of high accuracy combined with small network structures. Next, the applicability domain concept is suitably tailored and embedded into the proposed control structure in order to ensure that extrapolation is avoided in the controller predictions. Finally, an error correction term, estimating the error produced by the unmodeled dynamics and/or unmeasured external disturbances, is included to the control scheme to increase robustness. The resulting controller guarantees bounded input-bounded state (BIBS) stability for the closed loop system when the open loop system is BIBS stable. The proposed methodology is evaluated on two different control problems, namely, the control of an experimental armature-controlled direct current (DC) motor and the stabilization of a highly nonlinear simulated inverted pendulum. For each one of these problems, appropriate case studies are tested, in which a conventional neural controller employing inverse models and a PID controller are also applied. The results reveal the ability of the proposed control scheme to handle and manipulate diverse data through a data fusion approach and illustrate the superiority of the method in terms of faster and less oscillatory responses. Full article
(This article belongs to the Special Issue Soft Sensors and Intelligent Algorithms for Data Fusion)
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2380 KiB  
Article
Assessing the Health of LiFePO4 Traction Batteries through Monotonic Echo State Networks
by Luciano Sánchez, David Anseán, José Otero and Inés Couso
Sensors 2018, 18(1), 9; https://doi.org/10.3390/s18010009 - 21 Dec 2017
Cited by 12 | Viewed by 4214
Abstract
A soft sensor is presented that approximates certain health parameters of automotive rechargeable batteries from on-vehicle measurements of current and voltage. The sensor is based on a model of the open circuit voltage curve. This last model is implemented through monotonic neural networks [...] Read more.
A soft sensor is presented that approximates certain health parameters of automotive rechargeable batteries from on-vehicle measurements of current and voltage. The sensor is based on a model of the open circuit voltage curve. This last model is implemented through monotonic neural networks and estimate over-potentials arising from the evolution in time of the Lithium concentration in the electrodes of the battery. The proposed soft sensor is able to exploit the information contained in operational records of the vehicle better than the alternatives, this being particularly true when the charge or discharge currents are between moderate and high. The accuracy of the neural model has been compared to different alternatives, including data-driven statistical models, first principle-based models, fuzzy observers and other recurrent neural networks with different topologies. It is concluded that monotonic echo state networks can outperform well established first-principle models. The algorithms have been validated with automotive Li-FePO4 cells. Full article
(This article belongs to the Special Issue Soft Sensors and Intelligent Algorithms for Data Fusion)
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6360 KiB  
Article
COALA: A Protocol for the Avoidance and Alleviation of Congestion in Wireless Sensor Networks
by Dionisis Kandris, George Tselikis, Eleftherios Anastasiadis, Emmanouil Panaousis and Tasos Dagiuklas
Sensors 2017, 17(11), 2502; https://doi.org/10.3390/s17112502 - 31 Oct 2017
Cited by 19 | Viewed by 4440
Abstract
The occurrence of congestion has an extremely deleterious impact on the performance of Wireless Sensor Networks (WSNs). This article presents a novel protocol, named COALA (COngestion ALleviation and Avoidance), which aims to act both proactively, in order to avoid the creation [...] Read more.
The occurrence of congestion has an extremely deleterious impact on the performance of Wireless Sensor Networks (WSNs). This article presents a novel protocol, named COALA (COngestion ALleviation and Avoidance), which aims to act both proactively, in order to avoid the creation of congestion in WSNs, and reactively, so as to mitigate the diffusion of upcoming congestion through alternative path routing. Its operation is based on the utilization of an accumulative cost function, which considers both static and dynamic metrics in order to send data through the paths that are less probable to be congested. COALA is validated through simulation tests, which exhibit its ability to achieve remarkable reduction of loss ratios, transmission delays and energy dissipation. Moreover, the appropriate adjustment of the weighting of the accumulative cost function enables the algorithm to adapt to the performance criteria of individual case scenarios. Full article
(This article belongs to the Special Issue Soft Sensors and Intelligent Algorithms for Data Fusion)
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2017 KiB  
Article
Soft Sensing of Non-Newtonian Fluid Flow in Open Venturi Channel Using an Array of Ultrasonic Level Sensors—AI Models and Their Validations
by Khim Chhantyal, Håkon Viumdal and Saba Mylvaganam
Sensors 2017, 17(11), 2458; https://doi.org/10.3390/s17112458 - 26 Oct 2017
Cited by 9 | Viewed by 5129
Abstract
In oil and gas and geothermal installations, open channels followed by sieves for removal of drill cuttings, are used to monitor the quality and quantity of the drilling fluids. Drilling fluid flow rate is difficult to measure due to the varying flow conditions [...] Read more.
In oil and gas and geothermal installations, open channels followed by sieves for removal of drill cuttings, are used to monitor the quality and quantity of the drilling fluids. Drilling fluid flow rate is difficult to measure due to the varying flow conditions (e.g., wavy, turbulent and irregular) and the presence of drilling cuttings and gas bubbles. Inclusion of a Venturi section in the open channel and an array of ultrasonic level sensors above it at locations in the vicinity of and above the Venturi constriction gives the varying levels of the drilling fluid in the channel. The time series of the levels from this array of ultrasonic level sensors are used to estimate the drilling fluid flow rate, which is compared with Coriolis meter measurements. Fuzzy logic, neural networks and support vector regression algorithms applied to the data from temporal and spatial ultrasonic level measurements of the drilling fluid in the open channel give estimates of its flow rate with sufficient reliability, repeatability and uncertainty, providing a novel soft sensing of an important process variable. Simulations, cross-validations and experimental results show that feedforward neural networks with the Bayesian regularization learning algorithm provide the best flow rate estimates. Finally, the benefits of using this soft sensing technique combined with Venturi constriction in open channels are discussed. Full article
(This article belongs to the Special Issue Soft Sensors and Intelligent Algorithms for Data Fusion)
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1611 KiB  
Article
Alumina Concentration Detection Based on the Kernel Extreme Learning Machine
by Sen Zhang, Tao Zhang, Yixin Yin and Wendong Xiao
Sensors 2017, 17(9), 2002; https://doi.org/10.3390/s17092002 - 01 Sep 2017
Cited by 14 | Viewed by 4395
Abstract
The concentration of alumina in the electrolyte is of great significance during the production of aluminum. The amount of the alumina concentration may lead to unbalanced material distribution and low production efficiency and affect the stability of the aluminum reduction cell and current [...] Read more.
The concentration of alumina in the electrolyte is of great significance during the production of aluminum. The amount of the alumina concentration may lead to unbalanced material distribution and low production efficiency and affect the stability of the aluminum reduction cell and current efficiency. The existing methods cannot meet the needs for online measurement because industrial aluminum electrolysis has the characteristics of high temperature, strong magnetic field, coupled parameters, and high nonlinearity. Currently, there are no sensors or equipment that can detect the alumina concentration on line. Most companies acquire the alumina concentration from the electrolyte samples which are analyzed through an X-ray fluorescence spectrometer. To solve the problem, the paper proposes a soft sensing model based on a kernel extreme learning machine algorithm that takes the kernel function into the extreme learning machine. K-fold cross validation is used to estimate the generalization error. The proposed soft sensing algorithm can detect alumina concentration by the electrical signals such as voltages and currents of the anode rods. The predicted results show that the proposed approach can give more accurate estimations of alumina concentration with faster learning speed compared with the other methods such as the basic ELM, BP, and SVM. Full article
(This article belongs to the Special Issue Soft Sensors and Intelligent Algorithms for Data Fusion)
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3993 KiB  
Article
A Novel Online Sequential Extreme Learning Machine for Gas Utilization Ratio Prediction in Blast Furnaces
by Yanjiao Li, Sen Zhang, Yixin Yin, Wendong Xiao and Jie Zhang
Sensors 2017, 17(8), 1847; https://doi.org/10.3390/s17081847 - 10 Aug 2017
Cited by 56 | Viewed by 6016
Abstract
Gas utilization ratio (GUR) is an important indicator used to measure the operating status and energy consumption of blast furnaces (BFs). In this paper, we present a soft-sensor approach, i.e., a novel online sequential extreme learning machine (OS-ELM) named DU-OS-ELM, to establish a [...] Read more.
Gas utilization ratio (GUR) is an important indicator used to measure the operating status and energy consumption of blast furnaces (BFs). In this paper, we present a soft-sensor approach, i.e., a novel online sequential extreme learning machine (OS-ELM) named DU-OS-ELM, to establish a data-driven model for GUR prediction. In DU-OS-ELM, firstly, the old collected data are discarded gradually and the newly acquired data are given more attention through a novel dynamic forgetting factor (DFF), depending on the estimation errors to enhance the dynamic tracking ability. Furthermore, we develop an updated selection strategy (USS) to judge whether the model needs to be updated with the newly coming data, so that the proposed approach is more in line with the actual production situation. Then, the convergence analysis of the proposed DU-OS-ELM is presented to ensure the estimation of output weight converge to the true value with the new data arriving. Meanwhile, the proposed DU-OS-ELM is applied to build a soft-sensor model to predict GUR. Experimental results demonstrate that the proposed DU-OS-ELM obtains better generalization performance and higher prediction accuracy compared with a number of existing related approaches using the real production data from a BF and the created GUR prediction model can provide an effective guidance for further optimization operation. Full article
(This article belongs to the Special Issue Soft Sensors and Intelligent Algorithms for Data Fusion)
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1517 KiB  
Article
Just-in-Time Correntropy Soft Sensor with Noisy Data for Industrial Silicon Content Prediction
by Kun Chen, Yu Liang, Zengliang Gao and Yi Liu
Sensors 2017, 17(8), 1830; https://doi.org/10.3390/s17081830 - 08 Aug 2017
Cited by 17 | Viewed by 4142
Abstract
Development of accurate data-driven quality prediction models for industrial blast furnaces encounters several challenges mainly because the collected data are nonlinear, non-Gaussian, and uneven distributed. A just-in-time correntropy-based local soft sensing approach is presented to predict the silicon content in this work. Without [...] Read more.
Development of accurate data-driven quality prediction models for industrial blast furnaces encounters several challenges mainly because the collected data are nonlinear, non-Gaussian, and uneven distributed. A just-in-time correntropy-based local soft sensing approach is presented to predict the silicon content in this work. Without cumbersome efforts for outlier detection, a correntropy support vector regression (CSVR) modeling framework is proposed to deal with the soft sensor development and outlier detection simultaneously. Moreover, with a continuous updating database and a clustering strategy, a just-in-time CSVR (JCSVR) method is developed. Consequently, more accurate prediction and efficient implementations of JCSVR can be achieved. Better prediction performance of JCSVR is validated on the online silicon content prediction, compared with traditional soft sensors. Full article
(This article belongs to the Special Issue Soft Sensors and Intelligent Algorithms for Data Fusion)
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3638 KiB  
Article
The Ship Movement Trajectory Prediction Algorithm Using Navigational Data Fusion
by Piotr Borkowski
Sensors 2017, 17(6), 1432; https://doi.org/10.3390/s17061432 - 20 Jun 2017
Cited by 78 | Viewed by 8652
Abstract
It is essential for the marine navigator conducting maneuvers of his ship at sea to know future positions of himself and target ships in a specific time span to effectively solve collision situations. This article presents an algorithm of ship movement trajectory prediction, [...] Read more.
It is essential for the marine navigator conducting maneuvers of his ship at sea to know future positions of himself and target ships in a specific time span to effectively solve collision situations. This article presents an algorithm of ship movement trajectory prediction, which, through data fusion, takes into account measurements of the ship’s current position from a number of doubled autonomous devices. This increases the reliability and accuracy of prediction. The algorithm has been implemented in NAVDEC, a navigation decision support system and practically used on board ships. Full article
(This article belongs to the Special Issue Soft Sensors and Intelligent Algorithms for Data Fusion)
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2600 KiB  
Article
Feed-Forward Neural Network Prediction of the Mechanical Properties of Sandcrete Materials
by Panagiotis G. Asteris, Panayiotis C. Roussis and Maria G. Douvika
Sensors 2017, 17(6), 1344; https://doi.org/10.3390/s17061344 - 09 Jun 2017
Cited by 143 | Viewed by 8173
Abstract
This work presents a soft-sensor approach for estimating critical mechanical properties of sandcrete materials. Feed-forward (FF) artificial neural network (ANN) models are employed for building soft-sensors able to predict the 28-day compressive strength and the modulus of elasticity of sandcrete materials. To this [...] Read more.
This work presents a soft-sensor approach for estimating critical mechanical properties of sandcrete materials. Feed-forward (FF) artificial neural network (ANN) models are employed for building soft-sensors able to predict the 28-day compressive strength and the modulus of elasticity of sandcrete materials. To this end, a new normalization technique for the pre-processing of data is proposed. The comparison of the derived results with the available experimental data demonstrates the capability of FF ANNs to predict with pinpoint accuracy the mechanical properties of sandcrete materials. Furthermore, the proposed normalization technique has been proven effective and robust compared to other normalization techniques available in the literature. Full article
(This article belongs to the Special Issue Soft Sensors and Intelligent Algorithms for Data Fusion)
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337 KiB  
Article
A Weighted Belief Entropy-Based Uncertainty Measure for Multi-Sensor Data Fusion
by Yongchuan Tang, Deyun Zhou, Shuai Xu and Zichang He
Sensors 2017, 17(4), 928; https://doi.org/10.3390/s17040928 - 22 Apr 2017
Cited by 84 | Viewed by 6260
Abstract
In real applications, how to measure the uncertain degree of sensor reports before applying sensor data fusion is a big challenge. In this paper, in the frame of Dempster–Shafer evidence theory, a weighted belief entropy based on Deng entropy is proposed to quantify [...] Read more.
In real applications, how to measure the uncertain degree of sensor reports before applying sensor data fusion is a big challenge. In this paper, in the frame of Dempster–Shafer evidence theory, a weighted belief entropy based on Deng entropy is proposed to quantify the uncertainty of uncertain information. The weight of the proposed belief entropy is based on the relative scale of a proposition with regard to the frame of discernment (FOD). Compared with some other uncertainty measures in Dempster–Shafer framework, the new measure focuses on the uncertain information represented by not only the mass function, but also the scale of the FOD, which means less information loss in information processing. After that, a new multi-sensor data fusion approach based on the weighted belief entropy is proposed. The rationality and superiority of the new multi-sensor data fusion method is verified according to an experiment on artificial data and an application on fault diagnosis of a motor rotor. Full article
(This article belongs to the Special Issue Soft Sensors and Intelligent Algorithms for Data Fusion)
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1389 KiB  
Article
Zero-Sum Matrix Game with Payoffs of Dempster-Shafer Belief Structures and Its Applications on Sensors
by Xinyang Deng, Wen Jiang and Jiandong Zhang
Sensors 2017, 17(4), 922; https://doi.org/10.3390/s17040922 - 21 Apr 2017
Cited by 42 | Viewed by 5985
Abstract
The zero-sum matrix game is one of the most classic game models, and it is widely used in many scientific and engineering fields. In the real world, due to the complexity of the decision-making environment, sometimes the payoffs received by players may be [...] Read more.
The zero-sum matrix game is one of the most classic game models, and it is widely used in many scientific and engineering fields. In the real world, due to the complexity of the decision-making environment, sometimes the payoffs received by players may be inexact or uncertain, which requires that the model of matrix games has the ability to represent and deal with imprecise payoffs. To meet such a requirement, this paper develops a zero-sum matrix game model with Dempster–Shafer belief structure payoffs, which effectively represents the ambiguity involved in payoffs of a game. Then, a decomposition method is proposed to calculate the value of such a game, which is also expressed with belief structures. Moreover, for the possible computation-intensive issue in the proposed decomposition method, as an alternative solution, a Monte Carlo simulation approach is presented, as well. Finally, the proposed zero-sum matrix games with payoffs of Dempster–Shafer belief structures is illustratively applied to the sensor selection and intrusion detection of sensor networks, which shows its effectiveness and application process. Full article
(This article belongs to the Special Issue Soft Sensors and Intelligent Algorithms for Data Fusion)
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575 KiB  
Article
Sensing Attribute Weights: A Novel Basic Belief Assignment Method
by Wen Jiang, Miaoyan Zhuang, Chunhe Xie and Jun Wu
Sensors 2017, 17(4), 721; https://doi.org/10.3390/s17040721 - 30 Mar 2017
Cited by 21 | Viewed by 4549
Abstract
Dempster–Shafer evidence theory is widely used in many soft sensors data fusion systems on account of its good performance for handling the uncertainty information of soft sensors. However, how to determine basic belief assignment (BBA) is still an open issue. The existing methods [...] Read more.
Dempster–Shafer evidence theory is widely used in many soft sensors data fusion systems on account of its good performance for handling the uncertainty information of soft sensors. However, how to determine basic belief assignment (BBA) is still an open issue. The existing methods to determine BBA do not consider the reliability of each attribute; at the same time, they cannot effectively determine BBA in the open world. In this paper, based on attribute weights, a novel method to determine BBA is proposed not only in the closed world, but also in the open world. The Gaussian model of each attribute is built using the training samples firstly. Second, the similarity between the test sample and the attribute model is measured based on the Gaussian membership functions. Then, the attribute weights are generated using the overlap degree among the classes. Finally, BBA is determined according to the sensed attribute weights. Several examples with small datasets show the validity of the proposed method. Full article
(This article belongs to the Special Issue Soft Sensors and Intelligent Algorithms for Data Fusion)
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2948 KiB  
Article
Testing a Firefly-Inspired Synchronization Algorithm in a Complex Wireless Sensor Network
by Chuangbo Hao, Ping Song, Cheng Yang and Xiongjun Liu
Sensors 2017, 17(3), 544; https://doi.org/10.3390/s17030544 - 08 Mar 2017
Cited by 3 | Viewed by 4390
Abstract
Data acquisition is the foundation of soft sensor and data fusion. Distributed data acquisition and its synchronization are the important technologies to ensure the accuracy of soft sensors. As a research topic in bionic science, the firefly-inspired algorithm has attracted widespread attention as [...] Read more.
Data acquisition is the foundation of soft sensor and data fusion. Distributed data acquisition and its synchronization are the important technologies to ensure the accuracy of soft sensors. As a research topic in bionic science, the firefly-inspired algorithm has attracted widespread attention as a new synchronization method. Aiming at reducing the design difficulty of firefly-inspired synchronization algorithms for Wireless Sensor Networks (WSNs) with complex topologies, this paper presents a firefly-inspired synchronization algorithm based on a multiscale discrete phase model that can optimize the performance tradeoff between the network scalability and synchronization capability in a complex wireless sensor network. The synchronization process can be regarded as a Markov state transition, which ensures the stability of this algorithm. Compared with the Miroll and Steven model and Reachback Firefly Algorithm, the proposed algorithm obtains better stability and performance. Finally, its practicality has been experimentally confirmed using 30 nodes in a real multi-hop topology with low quality links. Full article
(This article belongs to the Special Issue Soft Sensors and Intelligent Algorithms for Data Fusion)
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