The Fault detection which is based on fuzzy modeling is investigated. Takagi-Sugeno (TS) fuzzy model can
be derived by structure and parameter identification, where only the input-output data of the identified system are available. In the structure identification step, Gustafson-Kessel clustering algorithm (GKCA) is used to detect clusters of different geometrical shapes in the data set and to obtain the point-wise membership function of the premise. In the parameter identification step, Unscented Kalman filter (UKF) is
used to estimate the parameters of the premise’s membership function. In the consequence part, Kalman filter (KF) algorithm is applied as a linear regression to estimate parameters of the TS model using the input-output data set. Then, the obtained fuzzy model is used to detect the fault. Simulations are provided to demonstrate the effectiveness of the theoretical results.
Hierarchical algorithms of quasi linear ARX Neural Networks for Identificatio...Yuyun Wabula
This document summarizes a research paper on hierarchical algorithms for training a quasi-linear ARX neural network model for identification of nonlinear systems. The key points are:
1) A hierarchical algorithm is proposed that first estimates the system using a linear sub-model and least squares estimation to obtain linear parameters. It then trains a neural network nonlinear sub-model to refine the errors of the linear sub-model.
2) The linear parameter estimates are fixed and used as biases for the neural network, which is trained to minimize the residual errors of the linear sub-model.
3) This hierarchical approach separates the identification into linear and nonlinear parts, allowing analysis of the system linearly while also capturing nonlinearities. The neural
Control chart pattern recognition using k mica clustering and neural networksISA Interchange
Automatic recognition of abnormal patterns in control charts has seen increasing demands nowadays in manufacturing processes. This paper presents a novel hybrid intelligent method (HIM) for recognition of the common types of control chart pattern (CCP). The proposed method includes two main modules: a clustering module and a classifier module. In the clustering module, the input data is first clustered by a new technique. This technique is a suitable combination of the modified imperialist competitive algorithm (MICA) and the K-means algorithm. Then the Euclidean distance of each pattern is computed from the determined clusters. The classifier module determines the membership of the patterns using the computed distance. In this module, several neural networks, such as the multilayer perceptron, probabilistic neural networks, and the radial basis function neural networks, are investigated. Using the experimental study, we choose the best classifier in order to recognize the CCPs. Simulation results show that a high recognition accuracy, about 99.65%, is achieved.
This document discusses feature selection algorithms and self-organizing maps (SOM). It begins by introducing concepts related to feature selection, including the curse of dimensionality and feature reduction. It then provides details on the branch and bound algorithm for feature selection, including its steps, properties, and an example application. Finally, it discusses the beam search algorithm for feature selection as an alternative to branch and bound, comparing their observations and recommendations.
A novel nonlinear missile guidance law against maneuvering targets is designed based on the principles of partial stability. It is demonstrated that in a real approach which is adopted with actual situations, each state of the guidance system must have a special behavior and asymptotic stability or exponential stability of all states is not realistic. Thus, a new guidance law is developed based on the partial stability theorem in such a way that the behaviors of states in the closed-loop system are in conformity with a real guidance scenario that leads to collision. The performance of the proposed guidance law in terms of interception time and control effort is compared with the sliding mode guidance law by means of numerical simulations.
Although fuzzy systems demonstrate their ability to
solve different kinds of problems in various applications, there is an increasing interest on developing solid mathematical implementations suitable for control applications such as that used in fuzzy logic controllers (FLC). It is well known that, wide range of parameters is needed to be specified before the construction of a fuzzy system. To simplify in a systematic way the design and construction of a general fuzzy system, and without loss for generality a full parameterization process for a singleton type FLC is proposed in this paper. The resented methodology is very helpful in developing a universal computing algorithm for a standard fuzzy like PID controllers. An illustrative example shows the simplicity of applying the new paradigm.
Bayesian-Network-Based Algorithm Selection with High Level Representation Fee...ITIIIndustries
A real-world intelligent system consists of three basic modules: environment recognition, prediction (or estimation), and behavior planning. To obtain high quality results in these modules, high speed processing and real time adaptability on a case by case basis are required. In the environment recognition module many different algorithms and algorithm networks exist with varying performance. Thus, a mechanism that selects the best possible algorithm is required. To solve this problem we are using an algorithm selection approach to the problem of natural image understanding. This selection mechanism is based on machine learning; a bottom-up algorithm selection from real-world image features and a top-down algorithm selection using information obtained from a high level symbolic world description and algorithm suitability. The algorithm selection method iterates for each input image until the high-level description cannot be improved anymore. In this paper we present a method of iterative composition of the high level description. This step by step approach allows us to select the best result for each region of the image by evaluating all the intermediary representations and finally keep only the best one.
Extended Fuzzy C-Means with Random Sampling Techniques for Clustering Large DataAM Publications
Big data are any data that you cannot load into your computer’s primary memory. Clustering is a primary
task in pattern recognition and data mining. We need algorithms that scale well with the data size. The former
implementation, literal Fuzzy C-Means is linear or serialized. FCM algorithm attempts to partition a finite collection
of n elements into collection of c fuzzy clusters. So, given a finite set of data, this algorithm returns a list of c cluster
centers. However it doesn't scale well and slows down with increase in the size of data and is thus impractical and
sometimes undesirable. In this paper, we propose an extended version of fuzzy c-means clustering algorithm by means of various random sampling techniques to study which method scales well for large or very large data.
2-DOF BLOCK POLE PLACEMENT CONTROL APPLICATION TO:HAVE-DASH-IIBTT MISSILEZac Darcy
In a multivariable servomechanism design, it is required that the output vector tracks a certain reference
vector while satisfying some desired transient specifications, for this purpose a 2DOF control law
consisting of state feedback gain and feedforward scaling gain is proposed. The control law is designed
using block pole placement technique by assigning a set of desired Block poles in different canonical forms.
The resulting control is simulated for linearized model of the HAVE DASH II BTT missile; numerical
results are analyzed and compared in terms of transient response, gain magnitude, performance
robustness, stability robustness and tracking. The suitable structure for this case study is then selected.
Hierarchical algorithms of quasi linear ARX Neural Networks for Identificatio...Yuyun Wabula
This document summarizes a research paper on hierarchical algorithms for training a quasi-linear ARX neural network model for identification of nonlinear systems. The key points are:
1) A hierarchical algorithm is proposed that first estimates the system using a linear sub-model and least squares estimation to obtain linear parameters. It then trains a neural network nonlinear sub-model to refine the errors of the linear sub-model.
2) The linear parameter estimates are fixed and used as biases for the neural network, which is trained to minimize the residual errors of the linear sub-model.
3) This hierarchical approach separates the identification into linear and nonlinear parts, allowing analysis of the system linearly while also capturing nonlinearities. The neural
Control chart pattern recognition using k mica clustering and neural networksISA Interchange
Automatic recognition of abnormal patterns in control charts has seen increasing demands nowadays in manufacturing processes. This paper presents a novel hybrid intelligent method (HIM) for recognition of the common types of control chart pattern (CCP). The proposed method includes two main modules: a clustering module and a classifier module. In the clustering module, the input data is first clustered by a new technique. This technique is a suitable combination of the modified imperialist competitive algorithm (MICA) and the K-means algorithm. Then the Euclidean distance of each pattern is computed from the determined clusters. The classifier module determines the membership of the patterns using the computed distance. In this module, several neural networks, such as the multilayer perceptron, probabilistic neural networks, and the radial basis function neural networks, are investigated. Using the experimental study, we choose the best classifier in order to recognize the CCPs. Simulation results show that a high recognition accuracy, about 99.65%, is achieved.
This document discusses feature selection algorithms and self-organizing maps (SOM). It begins by introducing concepts related to feature selection, including the curse of dimensionality and feature reduction. It then provides details on the branch and bound algorithm for feature selection, including its steps, properties, and an example application. Finally, it discusses the beam search algorithm for feature selection as an alternative to branch and bound, comparing their observations and recommendations.
A novel nonlinear missile guidance law against maneuvering targets is designed based on the principles of partial stability. It is demonstrated that in a real approach which is adopted with actual situations, each state of the guidance system must have a special behavior and asymptotic stability or exponential stability of all states is not realistic. Thus, a new guidance law is developed based on the partial stability theorem in such a way that the behaviors of states in the closed-loop system are in conformity with a real guidance scenario that leads to collision. The performance of the proposed guidance law in terms of interception time and control effort is compared with the sliding mode guidance law by means of numerical simulations.
Although fuzzy systems demonstrate their ability to
solve different kinds of problems in various applications, there is an increasing interest on developing solid mathematical implementations suitable for control applications such as that used in fuzzy logic controllers (FLC). It is well known that, wide range of parameters is needed to be specified before the construction of a fuzzy system. To simplify in a systematic way the design and construction of a general fuzzy system, and without loss for generality a full parameterization process for a singleton type FLC is proposed in this paper. The resented methodology is very helpful in developing a universal computing algorithm for a standard fuzzy like PID controllers. An illustrative example shows the simplicity of applying the new paradigm.
Bayesian-Network-Based Algorithm Selection with High Level Representation Fee...ITIIIndustries
A real-world intelligent system consists of three basic modules: environment recognition, prediction (or estimation), and behavior planning. To obtain high quality results in these modules, high speed processing and real time adaptability on a case by case basis are required. In the environment recognition module many different algorithms and algorithm networks exist with varying performance. Thus, a mechanism that selects the best possible algorithm is required. To solve this problem we are using an algorithm selection approach to the problem of natural image understanding. This selection mechanism is based on machine learning; a bottom-up algorithm selection from real-world image features and a top-down algorithm selection using information obtained from a high level symbolic world description and algorithm suitability. The algorithm selection method iterates for each input image until the high-level description cannot be improved anymore. In this paper we present a method of iterative composition of the high level description. This step by step approach allows us to select the best result for each region of the image by evaluating all the intermediary representations and finally keep only the best one.
Extended Fuzzy C-Means with Random Sampling Techniques for Clustering Large DataAM Publications
Big data are any data that you cannot load into your computer’s primary memory. Clustering is a primary
task in pattern recognition and data mining. We need algorithms that scale well with the data size. The former
implementation, literal Fuzzy C-Means is linear or serialized. FCM algorithm attempts to partition a finite collection
of n elements into collection of c fuzzy clusters. So, given a finite set of data, this algorithm returns a list of c cluster
centers. However it doesn't scale well and slows down with increase in the size of data and is thus impractical and
sometimes undesirable. In this paper, we propose an extended version of fuzzy c-means clustering algorithm by means of various random sampling techniques to study which method scales well for large or very large data.
2-DOF BLOCK POLE PLACEMENT CONTROL APPLICATION TO:HAVE-DASH-IIBTT MISSILEZac Darcy
In a multivariable servomechanism design, it is required that the output vector tracks a certain reference
vector while satisfying some desired transient specifications, for this purpose a 2DOF control law
consisting of state feedback gain and feedforward scaling gain is proposed. The control law is designed
using block pole placement technique by assigning a set of desired Block poles in different canonical forms.
The resulting control is simulated for linearized model of the HAVE DASH II BTT missile; numerical
results are analyzed and compared in terms of transient response, gain magnitude, performance
robustness, stability robustness and tracking. The suitable structure for this case study is then selected.
A Mathematical Programming Approach for Selection of Variables in Cluster Ana...IJRES Journal
The document presents a mathematical programming approach for selecting important variables in cluster analysis. It formulates a nonlinear binary model to minimize the distance between observations within clusters, using indicator variables to select important variables. The model is applied to a sample dataset of 30 observations across 5 variables, correctly identifying variables 3, 4 and 5 as most important for clustering the observations into two groups. The results are compared to an existing variable selection heuristic, with the mathematical programming approach achieving a 100% correct classification versus 97% for the other method.
FUZZY CONTROL OF A SERVOMECHANISM: PRACTICAL APPROACH USING MAMDANI AND TAKAG...ijfls
The main objective of this work is to propose two fuzzy controllers: one based on the Mamdani inference
method and another controller based on the Takagi- Sugeno inference method, both will be designed for
application in a position control system of a servomechanism. Some comparations between the methods
mentioned above will be made with regard to the performance of the system in order to identify the
advantages of the Takagi- Sugeno method in relation to the Mamdani method in the presence of
disturbances and nonlinearities of the system. Some results of simulation and practical application are
presented and results obtained showed that controllers based on Takagi- Sugeno method is more efficient
than controllers based on Mamdani method for this specific application.
Scalability has been an essential factor for any kind of computational algorithm while considering its performance. In this Big Data era, gathering of large amounts of data is becoming easy. Data analysis on Big Data is not feasible using the existing Machine Learning (ML) algorithms and it perceives them to perform poorly. This is due to the fact that the computational logic for these algorithms is previously designed in sequential way. MapReduce becomes the solution for handling billions of data efficiently. In this report we discuss the basic building block for the computations behind ML algorithms, two different attempts to parallelize machine learning algorithms using MapReduce and a brief description on the overhead in parallelization of ML algorithms.
PROTECTOR CONTROL PC-AODV-BH IN THE AD HOC NETWORKSZac Darcy
In this paper we deal with the protector control that which we used to secure AODV routing protocol in Ad
Hoc networks. The considered system can be vulnerable to several attacks because of mobility and absence
of infrastructure. While the disturbance is assumed to be of the black hole type, we purpose a control
named "PC-AODV-BH" in order to neutralize the effects of malicious nodes. Such a protocol is obtained by
coupling hash functions, digital signatures and fidelity concept. An implementation under NS2 simulator
will be given to compare our proposed approach with SAODV protocol, basing on three performance
metrics and taking into account the number of black hole malicious nodes.
IRJET- Domestic Water Conservation by IoT (Smart Home)IRJET Journal
This document discusses singular system identification for a constrained rigid robot model. It begins by introducing constrained robot models and noting they can be considered singular systems. It then discusses the importance of singular system equivalency in identification, as an inappropriate equivalency can cause large errors. The document proposes using strong equivalency to transform the constrained robot model before identification. It applies recursive least squares identification to the strongly equivalent system. Simulation results show this approach improves identification error convergence and output tracking compared to previous techniques for constrained robot models.
Heuristic approach to optimize the number of test cases for simple circuitsVLSICS Design
In this paper a new solution is proposed for testing simple stwo stage electronic circuits. It minimizes the number of tests to be performed to determine the genuinity of the circuit. The main idea behind the present research work is to identify the maximum number of indistinguishable faults present in the given circuit and minimize the number of test cases based on the number of faults that has been detected. Heuristic approach is used for test minimization part, which identifies the essential tests from overall test cases. From the results it is observed that, test minimization varies from 50% to 99% with the lowest one corresponding to a circuit with four gates .Test minimization is low in case of circuits with lesser input leads in gates compared to greater input leads in gates for the boolean expression with same number of symbols. Achievement of 99% reduction is due to the fact that the large number of tests find the same faults. The new approach is implemented for simple circuits. The results show potential for both smaller test sets and lower cpu times.
Symbol Based Modulation Classification using Combination of Fuzzy Clustering ...CSCJournals
Most of approaches for recognition and classification of modulation have been founded on modulated signal’s components. In this paper, we develop an algorithm using fuzzy clustering and consequently hierarchical clustering algorithms considering the constellation of the received signal to identify the modulation types of the communication signals automatically. The simulation that has been conducted shows high capability of this method for recognition of modulation levels in the presence of noise and also, this method is applicable to digital modulations of arbitrary size and dimensionality. In addition this classification finds the decision boundary of the signal which is critical information for bit detection.
EFFECT OF TWO EXOSYSTEM STRUCTURES ON OUTPUT REGULATION OF THE RTAC SYSTEMijctcm
This paper presents results on the output regulation of a single-input multi-output (SIMO) rotationaltranslational actuator (RTAC) system. The results focus primarily on stability and robustness, which are
studied in light of the presence of externally generated exogenous input signals. Two exosystem types were
investigated and tested. Obtained results answers the question of asymptotic stabilization and tracking of a
desired trajectory in the presence of a dynamic exosystem. The results confirmed the working theory of
robust stabilization using output feedback techniques, borne out of differential-geometric observer design
principles. The utilized design showed good stability results which compares favourably with existing
works on RTAC stabilization.
Financial Time Series Analysis Based On Normalized Mutual Information FunctionsIJCI JOURNAL
A method of predictability analysis of future values of financial time series is described. The method is based on normalized mutual information functions. In the analysis, the use of these functions allowed to refuse any restrictions on the distributions of the parameters and on the correlations between parameters. A comparative analysis of the predictability of financial time series of Tel Aviv 25 stock exchange has been carried out.
DOTNET 2013 IEEE CLOUDCOMPUTING PROJECT A fast clustering based feature subse...IEEEGLOBALSOFTTECHNOLOGIES
To Get any Project for CSE, IT ECE, EEE Contact Me @ 09849539085, 09966235788 or mail us - ieeefinalsemprojects@gmail.com-Visit Our Website: www.finalyearprojects.org
Single Channel Speech De-noising Using Kernel Independent Component Analysis...theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
A Combined Approach for Feature Subset Selection and Size Reduction for High ...IJERA Editor
selection of relevant feature from a given set of feature is one of the important issues in the field of
data mining as well as classification. In general the dataset may contain a number of features however it is not
necessary that the whole set features are important for particular analysis of decision making because the
features may share the common information‟s and can also be completely irrelevant to the undergoing
processing. This generally happen because of improper selection of features during the dataset formation or
because of improper information availability about the observed system. However in both cases the data will
contain the features that will just increase the processing burden which may ultimately cause the improper
outcome when used for analysis. Because of these reasons some kind of methods are required to detect and
remove these features hence in this paper we are presenting an efficient approach for not just removing the
unimportant features but also the size of complete dataset size. The proposed algorithm utilizes the information
theory to detect the information gain from each feature and minimum span tree to group the similar features
with that the fuzzy c-means clustering is used to remove the similar entries from the dataset. Finally the
algorithm is tested with SVM classifier using 35 publicly available real-world high-dimensional dataset and the
results shows that the presented algorithm not only reduces the feature set and data lengths but also improves the
performances of the classifier.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
A Modified KS-test for Feature SelectionIOSR Journals
This document proposes a modified Kolmogorov-Smirnov (KS) test-based feature selection algorithm. It begins with an overview of feature selection and its benefits. It then discusses two common feature selection approaches: filter and wrapper models. The document proposes a fast redundancy removal filter based on a modified KS statistic that utilizes class label information to compare feature pairs. It compares the proposed algorithm to other methods like Correlation Feature Selection (CFS) and KS-Correlation Based Filter (KS-CBF). The efficiency and effectiveness of the various methods are tested on standard classifiers. In most cases, the proposed approach achieved equal or better classification accuracy compared to using all features or the other algorithms.
Sensitivity analysis in a lidar camera calibrationcsandit
In this paper, variability analysis was performed o
n the model calibration methodology between
a multi-camera system and a LiDAR laser sensor (Lig
ht Detection and Ranging). Both sensors
are used to digitize urban environments. A practica
l and complete methodology is presented to
predict the error propagation inside the LiDAR-came
ra calibration. We perform a sensitivity
analysis in a local and global way. The local appro
ach analyses the output variance with
respect to the input, only one parameter is varied
at once. In the global sensitivity approach, all
parameters are varied simultaneously and sensitivit
y indexes are calculated on the total
variation range of the input parameters. We quantif
y the uncertainty behaviour in the intrinsic
camera parameters and the relationship between the
noisy data of both sensors and their
calibration. We calculated the sensitivity indexes
by two techniques, Sobol and FAST (Fourier
amplitude sensitivity test). Statistics of the sens
itivity analysis are displayed for each sensor, the
sensitivity ratio in laser-camera calibration data
Farsi character recognition using new hybrid feature extraction methodsijcseit
Identification of visual words and writings has long been one of the most essential and the most attractive
operations in the field of image processing which has been studied since the last few decades and includes
security, traffic control, fields of psychology, medicine, and engineering, etc. Previous techniques in the
field of identification of visual writings are very similar to each other for the most parts of their analysis,
and depending on the needs of the operational field have presented different feature extraction. Changes in
style of writing and font and turns of words and other issues are challenges of characters identifying
activity. In this study, a system of Persian character identification using independent orthogonal moment
that is Zernike Moment and Fourier-Mellin Moment has been used as feature extraction technique. The
values of Zernike Moments as characteristics independent of rotation have been used for classification
issues in the past and each of their real and imaginary components have been neglected individually and
with the phase coefficients, each of them will be changed by rotation. In this study, Zernike and Fourier-
Mellin Moments have been investigated to detect Persian characters in noisy and noise-free images. Also,
an improvement on the k-Nearest Neighbor (k-NN) classifier is proposed for character recognition. Using
the results comparison of the proposed method with current salient methods such as Back Propagation
(BP) and Radial Basis Function (RBF) neural networks in terms of feature extraction in words, it has been
shown that on the Hoda database, the proposed method reaches an acceptable detection rate (96/5%).
The Positive Effects of Fuzzy C-Means Clustering on Supervised Learning Class...Waqas Tariq
Selection of inputs is one of the most substantial components of classification algorithms for data mining and pattern recognition problems since even the best classifier will perform badly if the inputs are not selected very well. Big data and computational complexity are main cause of bad performance and low accuracy for classical classifiers. In other words, the complexity of classifier method is inversely proportional with its classification efficiency. For this purpose, two hybrid classifiers have been developed by using both type-1 and type-2 fuzzy c-means clustering with cascaded a classifier. In this proposed classifier, a large number of data points are reduced by using fuzzy c-means clustering before applied to a classifier algorithm as inputs. The aim of this study is to investigate the effect of fuzzy clustering on well-known and useful classifiers such as artificial neural networks (ANN) and support vector machines (SVM). Then the role of positive effects of these proposed algorithms were investigated on applied different data sets.
The Positive Effects of Fuzzy C-Means Clustering on Supervised Learning Class...CSCJournals
Selection of inputs is one of the most substantial components of classification algorithms for data mining and pattern recognition problems since even the best classifier will perform badly if the inputs are not selected very well. Big data and computational complexity are main cause of bad performance and low accuracy for classical classifiers. In other words, the complexity of classifier method is inversely proportional with its classification efficiency. For this purpose, two hybrid classifiers have been developed by using both type-1 and type-2 fuzzy c-means clustering with cascaded a classifier. In this proposed classifier, a large number of data points are reduced by using fuzzy c-means clustering before applied to a classifier algorithm as inputs. The aim of this study is to investigate the effect of fuzzy clustering on well-known and useful classifiers such as artificial neural networks (ANN) and support vector machines (SVM). Then the role of positive effects of these proposed algorithms were investigated on applied different data sets.
Cone Crusher Model Identification Using Block-Oriented Systems with Orthonorm...ijctcm
In this paper, block-oriented systems with linear parts based on Laguerre functions is used to approximation of a cone crusher dynamics. Adaptive recursive least squares algorithm is used to identification of Laguerre model. Various structures of Hammerstein, Wiener, Hammerstein-Wiener models are tested and the MATLAB simulation results are compared. The mean square error is used for models validation.It has been found that Hammerstein-Wiener with orthonormal basis functions improves the quality of approximation plant dynamics. The mean square error for this model is 11% on average throughout the considered range of the external disturbances amplitude. The analysis also showed that Wiener model cannot provide sufficient approximation accuracy of the cone crusher dynamics. During the process it is unstable due to the high sensitivity to disturbances on the output.The Hammerstein-Wiener model will be used to the design nonlinear model predictive control application
In this paper, block-oriented systems with linear parts based on Laguerre functions is used to
approximation of a cone crusher dynamics. Adaptive recursive least squares algorithm is used to
identification of Laguerre model. Various structures of Hammerstein, Wiener, Hammerstein-Wiener models
are tested and the MATLAB simulation results are compared. The mean square error is used for models
validation.It has been found that Hammerstein-Wiener with orthonormal basis functions improves the
quality of approximation plant dynamics. The mean square error for this model is 11% on average
throughout the considered range of the external disturbances amplitude. The analysis also showed that
Wiener model cannot provide sufficient approximation accuracy of the cone crusher dynamics. During the
process it is unstable due to the high sensitivity to disturbances on the output.The Hammerstein-Wiener
model will be used to the design nonlinear model predictive control application.
On Selection of Periodic Kernels Parameters in Time Series Prediction cscpconf
In the paper the analysis of the periodic kernels parameters is described. Periodic kernels can
be used for the prediction task, performed as the typical regression problem. On the basis of the
Periodic Kernel Estimator (PerKE) the prediction of real time series is performed. As periodic
kernels require the setting of their parameters it is necessary to analyse their influence on the
prediction quality. This paper describes an easy methodology of finding values of parameters of
periodic kernels. It is based on grid search. Two different error measures are taken into
consideration as the prediction qualities but lead to comparable results. The methodology was
tested on benchmark and real datasets and proved to give satisfactory results.
ON SELECTION OF PERIODIC KERNELS PARAMETERS IN TIME SERIES PREDICTIONcscpconf
In the paper the analysis of the periodic kernels parameters is described. Periodic kernels can
be used for the prediction task, performed as the typical regression problem. On the basis of the
Periodic Kernel Estimator (PerKE) the prediction of real time series is performed. As periodic
kernels require the setting of their parameters it is necessary to analyse their influence on the
prediction quality. This paper describes an easy methodology of finding values of parameters of
periodic kernels. It is based on grid search. Two different error measures are taken into
consideration as the prediction qualities but lead to comparable results. The methodology was
tested on benchmark and real datasets and proved to give satisfactory results.
A Mathematical Programming Approach for Selection of Variables in Cluster Ana...IJRES Journal
The document presents a mathematical programming approach for selecting important variables in cluster analysis. It formulates a nonlinear binary model to minimize the distance between observations within clusters, using indicator variables to select important variables. The model is applied to a sample dataset of 30 observations across 5 variables, correctly identifying variables 3, 4 and 5 as most important for clustering the observations into two groups. The results are compared to an existing variable selection heuristic, with the mathematical programming approach achieving a 100% correct classification versus 97% for the other method.
FUZZY CONTROL OF A SERVOMECHANISM: PRACTICAL APPROACH USING MAMDANI AND TAKAG...ijfls
The main objective of this work is to propose two fuzzy controllers: one based on the Mamdani inference
method and another controller based on the Takagi- Sugeno inference method, both will be designed for
application in a position control system of a servomechanism. Some comparations between the methods
mentioned above will be made with regard to the performance of the system in order to identify the
advantages of the Takagi- Sugeno method in relation to the Mamdani method in the presence of
disturbances and nonlinearities of the system. Some results of simulation and practical application are
presented and results obtained showed that controllers based on Takagi- Sugeno method is more efficient
than controllers based on Mamdani method for this specific application.
Scalability has been an essential factor for any kind of computational algorithm while considering its performance. In this Big Data era, gathering of large amounts of data is becoming easy. Data analysis on Big Data is not feasible using the existing Machine Learning (ML) algorithms and it perceives them to perform poorly. This is due to the fact that the computational logic for these algorithms is previously designed in sequential way. MapReduce becomes the solution for handling billions of data efficiently. In this report we discuss the basic building block for the computations behind ML algorithms, two different attempts to parallelize machine learning algorithms using MapReduce and a brief description on the overhead in parallelization of ML algorithms.
PROTECTOR CONTROL PC-AODV-BH IN THE AD HOC NETWORKSZac Darcy
In this paper we deal with the protector control that which we used to secure AODV routing protocol in Ad
Hoc networks. The considered system can be vulnerable to several attacks because of mobility and absence
of infrastructure. While the disturbance is assumed to be of the black hole type, we purpose a control
named "PC-AODV-BH" in order to neutralize the effects of malicious nodes. Such a protocol is obtained by
coupling hash functions, digital signatures and fidelity concept. An implementation under NS2 simulator
will be given to compare our proposed approach with SAODV protocol, basing on three performance
metrics and taking into account the number of black hole malicious nodes.
IRJET- Domestic Water Conservation by IoT (Smart Home)IRJET Journal
This document discusses singular system identification for a constrained rigid robot model. It begins by introducing constrained robot models and noting they can be considered singular systems. It then discusses the importance of singular system equivalency in identification, as an inappropriate equivalency can cause large errors. The document proposes using strong equivalency to transform the constrained robot model before identification. It applies recursive least squares identification to the strongly equivalent system. Simulation results show this approach improves identification error convergence and output tracking compared to previous techniques for constrained robot models.
Heuristic approach to optimize the number of test cases for simple circuitsVLSICS Design
In this paper a new solution is proposed for testing simple stwo stage electronic circuits. It minimizes the number of tests to be performed to determine the genuinity of the circuit. The main idea behind the present research work is to identify the maximum number of indistinguishable faults present in the given circuit and minimize the number of test cases based on the number of faults that has been detected. Heuristic approach is used for test minimization part, which identifies the essential tests from overall test cases. From the results it is observed that, test minimization varies from 50% to 99% with the lowest one corresponding to a circuit with four gates .Test minimization is low in case of circuits with lesser input leads in gates compared to greater input leads in gates for the boolean expression with same number of symbols. Achievement of 99% reduction is due to the fact that the large number of tests find the same faults. The new approach is implemented for simple circuits. The results show potential for both smaller test sets and lower cpu times.
Symbol Based Modulation Classification using Combination of Fuzzy Clustering ...CSCJournals
Most of approaches for recognition and classification of modulation have been founded on modulated signal’s components. In this paper, we develop an algorithm using fuzzy clustering and consequently hierarchical clustering algorithms considering the constellation of the received signal to identify the modulation types of the communication signals automatically. The simulation that has been conducted shows high capability of this method for recognition of modulation levels in the presence of noise and also, this method is applicable to digital modulations of arbitrary size and dimensionality. In addition this classification finds the decision boundary of the signal which is critical information for bit detection.
EFFECT OF TWO EXOSYSTEM STRUCTURES ON OUTPUT REGULATION OF THE RTAC SYSTEMijctcm
This paper presents results on the output regulation of a single-input multi-output (SIMO) rotationaltranslational actuator (RTAC) system. The results focus primarily on stability and robustness, which are
studied in light of the presence of externally generated exogenous input signals. Two exosystem types were
investigated and tested. Obtained results answers the question of asymptotic stabilization and tracking of a
desired trajectory in the presence of a dynamic exosystem. The results confirmed the working theory of
robust stabilization using output feedback techniques, borne out of differential-geometric observer design
principles. The utilized design showed good stability results which compares favourably with existing
works on RTAC stabilization.
Financial Time Series Analysis Based On Normalized Mutual Information FunctionsIJCI JOURNAL
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DOTNET 2013 IEEE CLOUDCOMPUTING PROJECT A fast clustering based feature subse...IEEEGLOBALSOFTTECHNOLOGIES
To Get any Project for CSE, IT ECE, EEE Contact Me @ 09849539085, 09966235788 or mail us - ieeefinalsemprojects@gmail.com-Visit Our Website: www.finalyearprojects.org
Single Channel Speech De-noising Using Kernel Independent Component Analysis...theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
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selection of relevant feature from a given set of feature is one of the important issues in the field of
data mining as well as classification. In general the dataset may contain a number of features however it is not
necessary that the whole set features are important for particular analysis of decision making because the
features may share the common information‟s and can also be completely irrelevant to the undergoing
processing. This generally happen because of improper selection of features during the dataset formation or
because of improper information availability about the observed system. However in both cases the data will
contain the features that will just increase the processing burden which may ultimately cause the improper
outcome when used for analysis. Because of these reasons some kind of methods are required to detect and
remove these features hence in this paper we are presenting an efficient approach for not just removing the
unimportant features but also the size of complete dataset size. The proposed algorithm utilizes the information
theory to detect the information gain from each feature and minimum span tree to group the similar features
with that the fuzzy c-means clustering is used to remove the similar entries from the dataset. Finally the
algorithm is tested with SVM classifier using 35 publicly available real-world high-dimensional dataset and the
results shows that the presented algorithm not only reduces the feature set and data lengths but also improves the
performances of the classifier.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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Sensitivity analysis in a lidar camera calibrationcsandit
In this paper, variability analysis was performed o
n the model calibration methodology between
a multi-camera system and a LiDAR laser sensor (Lig
ht Detection and Ranging). Both sensors
are used to digitize urban environments. A practica
l and complete methodology is presented to
predict the error propagation inside the LiDAR-came
ra calibration. We perform a sensitivity
analysis in a local and global way. The local appro
ach analyses the output variance with
respect to the input, only one parameter is varied
at once. In the global sensitivity approach, all
parameters are varied simultaneously and sensitivit
y indexes are calculated on the total
variation range of the input parameters. We quantif
y the uncertainty behaviour in the intrinsic
camera parameters and the relationship between the
noisy data of both sensors and their
calibration. We calculated the sensitivity indexes
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Farsi character recognition using new hybrid feature extraction methodsijcseit
Identification of visual words and writings has long been one of the most essential and the most attractive
operations in the field of image processing which has been studied since the last few decades and includes
security, traffic control, fields of psychology, medicine, and engineering, etc. Previous techniques in the
field of identification of visual writings are very similar to each other for the most parts of their analysis,
and depending on the needs of the operational field have presented different feature extraction. Changes in
style of writing and font and turns of words and other issues are challenges of characters identifying
activity. In this study, a system of Persian character identification using independent orthogonal moment
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values of Zernike Moments as characteristics independent of rotation have been used for classification
issues in the past and each of their real and imaginary components have been neglected individually and
with the phase coefficients, each of them will be changed by rotation. In this study, Zernike and Fourier-
Mellin Moments have been investigated to detect Persian characters in noisy and noise-free images. Also,
an improvement on the k-Nearest Neighbor (k-NN) classifier is proposed for character recognition. Using
the results comparison of the proposed method with current salient methods such as Back Propagation
(BP) and Radial Basis Function (RBF) neural networks in terms of feature extraction in words, it has been
shown that on the Hoda database, the proposed method reaches an acceptable detection rate (96/5%).
The Positive Effects of Fuzzy C-Means Clustering on Supervised Learning Class...Waqas Tariq
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The Positive Effects of Fuzzy C-Means Clustering on Supervised Learning Class...CSCJournals
Selection of inputs is one of the most substantial components of classification algorithms for data mining and pattern recognition problems since even the best classifier will perform badly if the inputs are not selected very well. Big data and computational complexity are main cause of bad performance and low accuracy for classical classifiers. In other words, the complexity of classifier method is inversely proportional with its classification efficiency. For this purpose, two hybrid classifiers have been developed by using both type-1 and type-2 fuzzy c-means clustering with cascaded a classifier. In this proposed classifier, a large number of data points are reduced by using fuzzy c-means clustering before applied to a classifier algorithm as inputs. The aim of this study is to investigate the effect of fuzzy clustering on well-known and useful classifiers such as artificial neural networks (ANN) and support vector machines (SVM). Then the role of positive effects of these proposed algorithms were investigated on applied different data sets.
Cone Crusher Model Identification Using Block-Oriented Systems with Orthonorm...ijctcm
In this paper, block-oriented systems with linear parts based on Laguerre functions is used to approximation of a cone crusher dynamics. Adaptive recursive least squares algorithm is used to identification of Laguerre model. Various structures of Hammerstein, Wiener, Hammerstein-Wiener models are tested and the MATLAB simulation results are compared. The mean square error is used for models validation.It has been found that Hammerstein-Wiener with orthonormal basis functions improves the quality of approximation plant dynamics. The mean square error for this model is 11% on average throughout the considered range of the external disturbances amplitude. The analysis also showed that Wiener model cannot provide sufficient approximation accuracy of the cone crusher dynamics. During the process it is unstable due to the high sensitivity to disturbances on the output.The Hammerstein-Wiener model will be used to the design nonlinear model predictive control application
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approximation of a cone crusher dynamics. Adaptive recursive least squares algorithm is used to
identification of Laguerre model. Various structures of Hammerstein, Wiener, Hammerstein-Wiener models
are tested and the MATLAB simulation results are compared. The mean square error is used for models
validation.It has been found that Hammerstein-Wiener with orthonormal basis functions improves the
quality of approximation plant dynamics. The mean square error for this model is 11% on average
throughout the considered range of the external disturbances amplitude. The analysis also showed that
Wiener model cannot provide sufficient approximation accuracy of the cone crusher dynamics. During the
process it is unstable due to the high sensitivity to disturbances on the output.The Hammerstein-Wiener
model will be used to the design nonlinear model predictive control application.
On Selection of Periodic Kernels Parameters in Time Series Prediction cscpconf
In the paper the analysis of the periodic kernels parameters is described. Periodic kernels can
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Periodic Kernel Estimator (PerKE) the prediction of real time series is performed. As periodic
kernels require the setting of their parameters it is necessary to analyse their influence on the
prediction quality. This paper describes an easy methodology of finding values of parameters of
periodic kernels. It is based on grid search. Two different error measures are taken into
consideration as the prediction qualities but lead to comparable results. The methodology was
tested on benchmark and real datasets and proved to give satisfactory results.
ON SELECTION OF PERIODIC KERNELS PARAMETERS IN TIME SERIES PREDICTIONcscpconf
In the paper the analysis of the periodic kernels parameters is described. Periodic kernels can
be used for the prediction task, performed as the typical regression problem. On the basis of the
Periodic Kernel Estimator (PerKE) the prediction of real time series is performed. As periodic
kernels require the setting of their parameters it is necessary to analyse their influence on the
prediction quality. This paper describes an easy methodology of finding values of parameters of
periodic kernels. It is based on grid search. Two different error measures are taken into
consideration as the prediction qualities but lead to comparable results. The methodology was
tested on benchmark and real datasets and proved to give satisfactory results.
Direct digital control scheme for controlling hybrid dynamic systems using AN...XiaoLaui
An Estimator Based Inverse Dynamics Controller (EBIDC), which utilizes an Artificial Neural Network (ANN) based state estimation scheme for nonlinear autonomous hybrid systems which are subjected to state disturbances and measurement noises that are stochastic in nature, is proposed in this paper. A salient feature of the proposed scheme is that it offers better state estimates and hence a better control of non-measurable state variables with a non linear approach in correcting the a priori estimates by avoiding statistical linearization involved in existing approaches based on derivative free estimation methods. Simulation results guarantees significant reduction in Integral Square Error (ISE) and standard deviation (σ) of error, between the controlled variable and set point and control signal computation time when compared with best existing related work based on Unscented Kalman Filter (UKF) and Ensembeled Kalman Filter (EnKF). Detailed analysis of the experimental results on real plant under different operating conditions such as servo and regulatory operations, initial condition mismatch, and different types of faults in the system, confirms robustness of proposed approach in these conditions and support the simulation results obtained. The main advantage of the proposed controller is that the control signal computation time is very much less than the selected sampling time of the process, so direct control of the plant is possible with this approach.
This document provides an overview of machine learning concepts including feature selection, dimensionality reduction techniques like principal component analysis and singular value decomposition, feature encoding, normalization and scaling, dataset construction, feature engineering, data exploration, machine learning types and categories, model selection criteria, popular Python libraries, tuning techniques like cross-validation and hyperparameters, and performance analysis metrics like confusion matrix, accuracy, F1 score, ROC curve, and bias-variance tradeoff.
2-DOF Block Pole Placement Control Application To: Have-DASH-IIBITT MissileZac Darcy
In a multivariable servomechanism design, it is required that the output vector tracks a certain reference
vector while satisfying some desired transient specifications, for this purpose a 2DOF control law
consisting of state feedback gain and feedforward scaling gain is proposed. The control law is designed
using block pole placement technique by assigning a set of desired Block poles in different canonical forms.
The resulting control is simulated for linearized model of the HAVE DASH II BTT missile; numerical
results are analyzed and compared in terms of transient response, gain magnitude, performance
robustness, stability robustness and tracking. The suitable structure for this case study is then selected.
2-DOF Block Pole Placement Control Application To: Have-DASH-IIBITT MissileZac Darcy
In a multivariable servomechanism design, it is required that the output vector tracks a certain reference
vector while satisfying some desired transient specifications, for this purpose a 2DOF control law
consisting of state feedback gain and feedforward scaling gain is proposed. The control law is designed
using block pole placement technique by assigning a set of desired Block poles in different canonical forms.
The resulting control is simulated for linearized model of the HAVE DASH II BTT missile; numerical
results are analyzed and compared in terms of transient response, gain magnitude, performance
robustness, stability robustness and tracking. The suitable structure for this case study is then selected.
SYSTEM IDENTIFICATION AND MODELING FOR INTERACTING AND NON-INTERACTING TANK S...ijistjournal
System identification from the experimental data plays a vital role for model based controller design. Derivation of process model from first principles is often difficult due to its complexity. The first stage in the development of any control and monitoring system is the identification and modeling of the system. Each model is developed within the context of a specific control problem. Thus, the need for a general system identification framework is warranted. The proposed framework should be able to adapt and emphasize different properties based on the control objective and the nature of the behavior of the system. Therefore, system identification has been a valuable tool in identifying the model of the system based on the input and output data for the design of the controller. The present work is concerned with the identification of transfer function models using statistical model identification, process reaction curve method, ARX model, genetic algorithm and modeling using neural network and fuzzy logic for interacting and non interacting tank process. The identification technique and modeling used is prone to parameter change & disturbance. The proposed methods are used for identifying the mathematical model and intelligent model of interacting and non interacting process from the real time experimental data.
SYSTEM IDENTIFICATION AND MODELING FOR INTERACTING AND NON-INTERACTING TANK S...ijistjournal
System identification from the experimental data plays a vital role for model based controller design. Derivation of process model from first principles is often difficult due to its complexity. The first stage in the development of any control and monitoring system is the identification and modeling of the system. Each model is developed within the context of a specific control problem. Thus, the need for a general system identification framework is warranted. The proposed framework should be able to adapt and emphasize different properties based on the control objective and the nature of the behavior of the system. Therefore, system identification has been a valuable tool in identifying the model of the system based on the input and output data for the design of the controller. The present work is concerned with the identification of transfer function models using statistical model identification, process reaction curve method, ARX model, genetic algorithm and modeling using neural network and fuzzy logic for interacting and non interacting tank process. The identification technique and modeling used is prone to parameter change & disturbance. The proposed methods are used for identifying the mathematical model and intelligent model of interacting and non interacting process from the real time experimental data.
Q UANTUM C LUSTERING -B ASED F EATURE SUBSET S ELECTION FOR MAMMOGRAPHIC I...ijcsit
In this paper, we present an algorithm for feature selection. This algorithm labeled QC-FS: Quantum
Clustering for Feature Selection performs the selection in two steps. Partitioning the original features
space in order to group similar features is performed using the Quantum Clustering algorithm. Then the
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coefficient (CC) and the mutual information (MI). The feature which maximizes this information is chosen
by the algorithm
An Automatic Clustering Technique for Optimal ClustersIJCSEA Journal
This document presents a new automatic clustering algorithm called Automatic Merging for Optimal Clusters (AMOC). AMOC is a two-phase iterative extension of k-means clustering that aims to automatically determine the optimal number of clusters for a given dataset. In the first phase, AMOC initializes a large number of clusters k using k-means. In the second phase, it iteratively merges the lowest probability cluster with its closest neighbor, recomputing metrics each time to evaluate if the merge improved clustering quality. The algorithm stops merging once no improvements are found. Experimental results on synthetic and real datasets show AMOC finds nearly optimal cluster structures in terms of number, compactness and separation of clusters.
Dynamic Kohonen Network for Representing Changes in InputsJean Fecteau
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This document summarizes an academic paper that proposes modifying well-known local linear models for system identification by replacing their original recursive learning rules with outlier-robust variants based on M-estimation. It describes three existing local linear models - local linear map (LLM), radial basis function network (RBFN), and local model network (LMN) - and then introduces the concept of M-estimation as a way to make the learning rules of these models more robust to outliers. The performance of the proposed outlier-robust variants is evaluated on three benchmark datasets and is found to provide considerable improvement in the presence of outliers compared to the original models.
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State Estimation based Inverse Dynamic Controller for Hybrid system using Art...XiaoLaui
Authors have proposed State Estimation Based Inverse Dynamics Controller (SEBIDC), which utilizes an Artificial Neural Network (ANN) based state estimation scheme for nonlinear autonomous hybrid systems which are subjected to state disturbances and measurement noises that are stochastic in nature. A salient feature of the proposed scheme is that it offers better state estimates and hence a better control of non-measurable state variables with a non linear approach in correcting the a priori estimates by avoiding statistical linearization involved in existing approaches based on derivative free estimation methods. Simulation results guarantees significant reduction in Integral Square Error (ISE) and standard deviation (σ) of error, between the controlled variable and set point and control signal computation time when compared with best existing related work based on Unscented Kalman Filter (UKF) and Ensemble Kalman Filter (EnKF). Detailed analysis of the experimental results on real plant under different operating conditions such as servo and regulatory operations, initial condition mismatch, and different types of faults in the system, confirms robustness of proposed approach in these conditions and support the simulation results obtained. The main advantage of the proposed controller is that the control signal computation time is very much less than the selected sampling time of the process, so direct control of the plant is possible with this approach.
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1. Circuits and Systems: An International Journal (CSIJ), Vol. 1, No.3, July 2014
1
Fault detection based on novel fuzzy modelling
Zhen Luo 1,2,
Huajing Fang 2
,Xiaoyong Liu 2
and Xuquan Chen 1
,2
1
Guangxi Special Equipment Supervision and Inspection Institute, Guangxi 530219, P.
R. China
2
Department of Control Science and Engineering, Huazhong University of Science and
Technology, Wuhan 430074, P. R. China
ABSTRACT
The Fault detection which is based on fuzzy modeling is investigated. Takagi-Sugeno (TS) fuzzy model can
be derived by structure and parameter identification, where only the input-output data of the identified
system are available. In the structure identification step, Gustafson-Kessel clustering algorithm (GKCA) is
used to detect clusters of different geometrical shapes in the data set and to obtain the point-wise
membership function of the premise. In the parameter identification step, Unscented Kalman filter (UKF) is
used to estimate the parameters of the premise’s membership function. In the consequence part, Kalman
filter (KF) algorithm is applied as a linear regression to estimate parameters of the TS model using the
input-output data set. Then, the obtained fuzzy model is used to detect the fault. Simulations are provided to
demonstrate the effectiveness of the theoretical results.
KEYWORDS
Unscented Kalman filter, Kalman filter, data driven, Gustafson-Kessel clustering algorithm, fuzzy
modeling, fault detection
1. INTRODUCTION
Since fault detection (FD) &diagnosis technique is essential to improve the safety and reliability
of dynamic systems, recently more and more attention has been paid to FD. Many FD methods
have been developed to detect and identify sensor and actuator faults, such as analytical
redundancy [1-3], a neural network [4], parameter identification method based on Fourier
Transform [5], testing the covariance matrix of the innovation sequence [5], testing the eigen
values of the sample covariance matrix [6]. All of these methods mentioned above are based upon
model. Models with good accuracy are necessary to improve the correct diagnostic of faults.
However, with the rapid development of industrial technology, the modern industrial processes
have become more and more complicated and large-scale. It is thus difficult to construct an
effective and explicit physical model to characterize these dynamical systems. Sometimes, it is
even impossible to model nonlinear systems by analytical equations [7]. Here, the fuzzy modeling
has been extensively used to model complex nonlinear system through a set of measured input-
output data [8]. The Takagi-Sugeno (TS) model, which uses the fuzzy modeling technique,
approximate the nonlinear system by smoothly interpolating affine local models. Each local
model contributes to the global model in a fuzzy subset of the space characterized by a
membership function [9]. Then, based on the established system model, FD can be carried out.
A TS fuzzy model is usually constructed in three steps:
2. Circuits and Systems: An International Journal (CSIJ), Vol. 1, No.3, July 2014
2
Step 1: fuzzy clustering
Among various clustering algorithm, the Gustafson-Kessel clustering algorithm (GKCA) [10] has
been widely studied and applied by many researchers. The Gustafson-Kessel (GK) algorithm,
which is the fuzzy generalization of the Adaptive Distance Dynamic Clusters algorithm, searches
for ellipsoidal clusters. An advantage of the GK algorithm over Fuzzy C-means (FCM) [11] is
that GK can detect clusters of different shape and orientation in one data set.
Multidimensional fuzzy sets can be derived by clustering in the product space, but they are
generally difficult to be dealt with. In order to solve this problem, projected one-dimensional
fuzzy sets are usually preferred.
Step 2: estimate the parameters of the premise’s membership function
In order to obtain a fuzzy model, the premise’s membership functions must be expressed in a
form that allows computation of the membership degrees for input data not contained in the data
set. Each update estimation of the parameter vector corresponding to a nonlinear equation is
computed from the previous estimate and the new input data (here the input data are the point-
wise values of the membership function). To achieve this step, Unscented Kalman filter (UKF) is
used to approximate the point-wise defined membership functions by some suitable nonlinear
functions, for example normal function. The UKF as an improvement to the extended Kalman
filter (EKF) is one of the most widely used approach to analyze the stochastic nonlinear systems
[12]. This method is based on the unscented transform (UT) technique, a mechanism for
propagating mean and covariance through a nonlinear transformation [13, 14]. The state vector is
represented by a minimal set of carefully chosen sample points, called sigma points, which
approximate the posterior mean and covariance of the Gaussian random variable with a second
order accuracy[15, 16]. In contrast, the linearization technique used in the EKF can only achieve
first order accuracy. Generally, the prediction accuracy of UKF is better than EKF when the
model is highly nonlinear. The UKF has the same level of computational complexity as that of
EKF, both of which are within the order ( 3)
O L . Furthermore, Since the nonlinear models are
used without linearization, the UKF is not necessary to compute the Jacobian or Hessians
matrices [17, 18].
Step 3: estimation of the TS parameters
For linear dynamic systems with white process and measurement noise, the Kalman filter is an
optimal estimator [19]. The KF is used as a linear regression to efficiently choose the parameter
values of the consequent part (TS parameters) of the fuzzy model from the input-output data of
the identified system.
[20] proposes a fuzzy-modeling scheme combining GKCA and KF. GKCA is used to detect
clusters of different geometrical shapes in the data set and to obtain the point-wise membership
functions of the premise. After that, a KF is first used to estimate the parameters of the premise’s
membership function. Then, the KF is also used as a linear regression to efficiently choose the
parameter values of the consequent part (TS parameters) of the fuzzy model from the input-output
data of the identified system. KF process is a linear recursive minimum mean-square estimation
procedure. However, it can only deal with linear equation. In this sense, in order to obtain the
linear part, α -cut of the considered membership function is taken. Obviously, there are some
drawbacks with this algorithm
3. Circuits and Systems: An International Journal (CSIJ), Vol. 1, No.3, July 2014
3
In order to obtain membership function for the premise’s fuzzy sets, the multidimensional fuzzy
set defined point-wise in the row of the partition matrix is projected onto the regressor. Division
of each membership function into two sets ( sets are obtained for each regressor and sets are
obtained for all regressors). It needs large amount of computation
The selection of α relies entirely on experience. Too much or too small will influence on
membership function approximation. Moreover, the cut data causes the loss of useful
information.
The straight line which is used to approximate each set is not very good fit of the data.
In this paper, we point-wise define the premise membership function for the regressor, each
membership function as a sets (c sets are obtained for each regressor and cn sets are obtained for
all regressors). This will halve the amount of computation. Obviously, it is more accurate to
approximate the point-wise defined membership function by some suitable nonlinear function.
UKF is utilized to approximate the nonlinear function. A common FD approach is to keep
tracking residuals of measurement and compare them against a set threshold value. The residual
can be generated by the comparison of actual sample points and estimated sample points .
The structure of this paper is as follow. In section 2, the TS fuzzy models principle is
summarized. Section 3 gives new fuzzy modeling algorithm. Fault detection is presented in
section 4. Section 5 presents some simulation results. Conclusions are given in section 6.
2. TS FUZZY MODELS
In this section, the TS fuzzy models principle is summarized. The TS fuzzy model can represent
or model any unknown nonlinear system ( )
y f x
= , on the basis of some available input-output
data 1 2
[ , ..., ]T
t t t nt
x x x x
= and t
y .
In the TS fuzzy model, the rule consequents are crisp function of the model inputs
i
R : if x is ( )
i
A x , then 1,2,...,
T
i i i
y a x b i c
= + = (1)
where is the dimensional input invariable,is the output invariable. and are the dimensional
TS parameters. denotes the th rule and is the number of rules in the rule base. is the premise
multivariable membership function of the th rule. is the parameter vector of the th rule
Multi dimensional fuzzy sets can be derived by clustering in the product space. But it is generally
difficult to be interpreted, so projected one-dimensional fuzzy sets are usually preferred.
The TS fuzzy system is described as a set ofc fuzzy rules where the i th rule is as follows:
i
R : if 1
x is 1 1
( )
i
A x and …and n
x is ( )
in n
A x , then 1,2,...,
T
i i i
y a x b i c
= + = (2)
The final output of the TS fuzzy model for an arbitrary input sample can be calculated using the
following expression:
4. Circuits and Systems: An International Journal (CSIJ), Vol. 1, No.3, July 2014
4
1
1
( )( )
( )
c
T
i i i
i
c
i
i
x a x b
y
x
β
β
=
=
+
=
∑
∑
)
(3)
where ( )
i x
β represent the firing strength of the i th rule, and it has calculated by the following
equation:
1
( ) ij
n
i A
j
x
β µ
=
= ∏ (4)
ij
A
µ is the membership function of the fuzzy set ij
A .
3. NEW FUZZY MODELING ALGORITHM
The loop of establishing and training T-S fuzzy model by Gustafson-Kessel clustering
algorithm (GKCA) and UKF is as follows:
Fig.1 Flow chat of the new fuzzy modelling
Yes
Start
c=2
GKC
KF for
consequence
parameters
UKF for premise
membership
function
Performanc
es
End
No
c=c+
1
5. Circuits and Systems: An International Journal (CSIJ), Vol. 1, No.3, July 2014
5
A detailed description of the algorithm is provided next.
1. From the input–output sequences 1
{( , )}N
k k t
x y = , partition the data into a set of local
linear submodels by using GKCA in the product space X Y
× .
2. Obtain the membership functions for the premise variables by using cluster projections
and UKF.
Estimate the consequent parameters by KF algorithm.
3.1 FUZZY CLUSTERING
Fuzzy clustering is an important tool to identify the structure in data. The Gustafson-Kessel(GK)
algorithm, which is the fuzzy generalization of the Adaptive Distance Dynamic Clusters
algorithm, searches for ellipsoidal clusters. An advantage of the GK algorithm over Fuzzy C-
means (FCM) is that GK can detect clusters of different shape and orientation in one data set.
The original objective functional for the GK algorithm is the following:
1 1
( ) ( )
c N
m T
it t i i t i
i t
J z v M z v
µ
= =
= − −
∑∑ (5)
The following restrictions hold
1
1 1
N
m
it
t
t N
µ
=
= ≤ ≤
∑
(6)
where is a positive-definite symmetric matrix related to the covariance matrix of the th
prototype, is a weighting exponent that determines the fuzziness of the resulting cluster(for a
crisp , fuzzy model , but typically ). is the number of data points, is the number clusters, is the
th data point, is the th cluster centre, is the degree of the membership of the th data point in the
th cluster centre.
3.2 PREMISE MEMBERSHIP FUNCTION
UKF as an improvement to extended Kalman filter (EKF) is the most widely used approach to
analyze the stochastic nonlinear system and show good performance in many cases[12]. In this
sense, we propose to use UKF as a nonlinear regression as follow: consider cn sets, each set
represents the nonlinear part of the point-wise set of a certain premise’s membership function (for
example Gauss type membership function). So we obtaincn parameter vector. In each set, we will
have j
N data (samples), where j denotes the j th set.
Then, each set can be modeled by the following measurement equation
6. Circuits and Systems: An International Journal (CSIJ), Vol. 1, No.3, July 2014
6
2
2
( , ) 1,2...
( )
exp( ) 1,2...
2
j j j j
t t t
j j
j
t
t j
j
A h x v j cn
x d
v t N
θ
σ
= + =
−
= − + =
(7)
where [ , ]
j j j
d
θ σ
= is the parameters vector, j
t
v is the measurement noise, j
N is the number of
data(samples) in the j th set and the j denotes the j th nonlinear regression.
j
θ will be considered as a state variable, so the state equation will be
1 1
j j j j
t t t
F w
θ θ − −
= + (8)
where is the value of the state variable at the moment , is the state noise, is the state transition
matrix we assume that and are uncorrelated zero mean Gaussian random vectors and their
covariance matrices are and
The procedure for implementing the UKF can be summarized as follows:
Step 1: sigma points calculation
1 1 1 1
[ , ( ) ]
j j j
t t t t
n P
χ θ θ λ
− − − −
= ± +
) ) )
(9)
Step 2: prediction
| 1 1
j j j
t t t
F
χ χ
− −
=
| 1 1| 1
j j j
t t t t
F
θ θ
− − −
=
) )
| 1 1| 1
j j j jT
t t t t
P F P F Q
− − −
= +
)
(10)
Step 3: update.
| 1 | 1
( )
j j
t t t t
A h θ
− −
=
) )
| 1 | 1
( )
j j
l t t l t t
h
γ χ
− −
=
2
| 1 | 1 | 1 | 1
0
( )( )
j j
t t
n
j c j j j j T
l l t t t t l t t t t
A A
l
P A A R
ω γ γ
− − − −
=
= − − +
∑
) )
)
2
| 1 | 1 | 1
0
( )( )
j j
t t
n
j c j j j j T
l t t t l t t t t
A
l
P A R
θ
ω χ θ γ
− − −
=
= − − +
∑
) )
)
7. Circuits and Systems: An International Journal (CSIJ), Vol. 1, No.3, July 2014
7
1
j j j j
t t t t
j j
t A A A
K P P
θ
−
=
) )
| 1 | 1
( )
j j j j
t t t t t t t
K A A
θ θ − −
= + −
) ) )
1
| 1 j j
t t
j T
t t t t t
A A
P P K P K
−
−
= −
) ) )
(11)
where, 2
0 / ( ) (1 )
c
n
ω λ λ α β
= + + − + , / 2( ) 1...2
m c
l l n l n
ω ω λ λ
= = + = , 2
( 1)
n
λ α
= − . c
l
ω is a set
of scalar weights, and n is the state dimension; the parameter α determines the spread of
the sigma points around x
)
and is usually set to 1 4 1
e α
− ≤ ≤ , The constant β is used to
incorporate part of the prior knowledge of the distribution of x , and for Gaussian
distributions, 2
β = is optimal.
Often it is expected that the system parameters do not vary or, if they do, the variation is
much slower than that of the system state. So, we will take j
F I
= .
3.3 ESTIMATION CONSEQUENT PARAMETERS
In this section, KF algorithm is used to compute the consequent parameters from the data
set and the estimated premise’s membership functions.
From (3), we have
1
( )( )
c
T
i i i
i
y x a x b
ψ
=
= +
∑
) (12)
where
1
( )
( )
( )
i
i c
i
i
x
x
x
β
ψ
β
=
=
∑ is the normalized activation value of the i th rule.
[ ] [ ] [ ] [ ]
1 2 1 1
( ) 1 ( ) 1 ... ( ) 1 ...
T
c c c
y x x x x x x a b a b
ψ ψ ψ
=
)
[ ]
1 1...
T
c c
a b a b
Φ = , [ ] [ ] [ ]
1 2
( ) 1 ( ) 1 ... ( ) 1
c
x x x x x x
ψ ψ ψ
Ω = (13)
The measurement equation can be taken as the following form
t t t
y v
= Ω Φ +
) (14)
Then, j
θ will be considered as a state variable, so the state equation will be
8. Circuits and Systems: An International Journal (CSIJ), Vol. 1, No.3, July 2014
8
1 1
t t t
F w
− −
Φ = Φ + (15)
Now, we can use KF to estimate the TS parameter vector t
Φ as follows:
| 1 1| 1
t t t t
F
− − −
Φ = Φ
) )
| 1 1| 1
T
t t t t
P FP F Q
− − −
= +
1
| 1 | 1
( )
T T
t t t t t t t t
K P P R −
− −
= Ω Ω Ω +
| | 1 | 1
( )
t t t t t t t t t
K y
− −
Φ = Φ + −Ω Φ
) ) )
| | 1 | 1
t t t t t t t t
P P K P
− −
= − Ω (16)
where t
Φ
)
is the estimated value of t
Φ . Also, we will take F I
= .
4. PROCESS FAULT DETECTION
The fuzzy FD system is based on fuzzy models identified directly from data. A model is used to
estimate the nominal output signals.
y y
∆ = −
)
(17)
where y is the output of the system and y
)
is the output of the model in normal operation. When
any component of ∆ is bigger than a certain threshold, the system detects a fault.
5.SIMULATION
The sampling period of training data and testing data are all 0.05h. We choose 800 data points
without fault and 600 data points with fault 1 after collecting 200 data points without fault. The
number of clusters 12
c = .
0 100 200 300 400 500 600 700 800 900
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
membership
9. Circuits and Systems: An International Journal (CSIJ), Vol. 1, No.3, July 2014
9
Fig.2 the red solid line indicates the actual membership function, the black dotted line indicates
the premise membership function based on UKF, the blue dashed line indicates the premise
membership function based on KF
Fig.3 the actual sample point without fault and estimated sample point without fault
Fig.4 the residual with fault
Fig.5 the actual sample point without fault and the estimated sample point with fault
0 100 200 300 400 500 600 700 800 900
0.185
0.19
0.195
0.2
0.205
0.21
0.215
0.22
0.225
0.23
0.235
no fault model output
sampling point
variable
NO
1
estimated value without fault
actual value without fault
0 100 200 300 400 500 600 700 800 900
0
0.005
0.01
0.015
sampling point
residual
0 100 200 300 400 500 600 700 800 900
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
sampling point
variable
NO
1
actual value without fault
estimated value with fault
10. Circuits and Systems: An International Journal (CSIJ), Vol. 1, No.3, July 2014
10
Fig.6 the residual with fault
The membership functions is given in Fig.2. The red solid line indicates the actual membership
function, the black dotted line indicates the premise membership function based on UKF, the blue
dashed line indicates the premise membership function based on KF. It can be seen from the
figure that both approaches track the true state. However, the obtained premise membership based
on UKF is more close to the true value than based on KF. It means that estimating the premise
membership based on UKF is superior to based on KF.
In Fig.3, we can see that the actual sample point can be tracked well by the estimated sample
point. Fig.4 shows that the absolute value of the residuals which is derived by subtracting the
estimated value of the actual value is lower than the threshold. The simulation results consistent
with the actual case.
When the fault 1 occurs at the step 200, the simulation results are given in Fig.5-6. The estimated
sample points have deviated from actual sample points after 200 steps in Fig5 due to the fault, but
the actual sample point can be tracked well by the estimated sample point after the step 500
because of feedback effect. The fault makes absolute value of the residuals exceed the threshold
at step 206 which is given in Fig.6. I.e. the fault can be detected after occurrence of 6 steps.
6.CONCLUSION
In this paper, a fault detection algorithm based on data driven is proposed. The proposed
algorithm is composed of two steps: (1) fuzzy modeling contain fuzzy clustering, determination
of premise membership functions and TS parameters. (2) Fault detection based on the established
model. In the first step, a fuzzy modeling scheme on the basis of the GKCA and UKF to estimate
the premise membership, KF is used to estimate the TS parameter. The performances of the
proposed algorithm are demonstrated on the TE challenge problem.
0 100 200 300 400 500 600 700 800 900
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
detection of the occurance of the fault
sampling point
r
e
s
id
u
a
l
residual
threshold
11. Circuits and Systems: An International Journal (CSIJ), Vol. 1, No.3, July 2014
11
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12. Circuits and Systems: An International Journal (CSIJ), Vol. 1, No.3, July 2014
Authors
Zhen Luo She was born in 1983. Sh
Science and Technology. Her research interests include
and fault diagnosis of networked control sys
Huajing Fang was born in 1955. He is
and Technology. His research interests
dynamics and control of autonomous
control.
Xuquan Chen was born in 1984.
Science and Technology. His research interest is signal processing.
Circuits and Systems: An International Journal (CSIJ), Vol. 1, No.3, July 2014
She is a Ph.D. candidate in Huazhong University of
research interests include Kalman filtering state estimation
networked control sys tems.
was born in 1955. He is a Professor in Huazhong University of Science
His research interests include complex networked control systems,
mous vehicle’s swarm, fault diagnosis and fault-tolerant
was born in 1984. he is a Ph.D. candidate in Huazhong University of
Science and Technology. His research interest is signal processing.
Circuits and Systems: An International Journal (CSIJ), Vol. 1, No.3, July 2014
12