scholarly journals Intelligent Ball Bearing Fault Diagnosis Using Fractional Lorenz Chaos Extension Detection

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 3069 ◽  
Author(s):  
An-Hong Tian ◽  
Cheng-Biao Fu ◽  
Yu-Chung Li ◽  
Her-Terng Yau
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Element Model ◽  
Extension Theory ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Bearing Fault Diagnosis ◽  
Dynamic Errors ◽  
Chaos System ◽  
Matter Element Model

In this study we used a non-autonomous Chua’s circuit, and the fractional Lorenz chaos system. This was combined with the Extension theory detection method to analyze the voltage signals. The bearing vibration signals, measured using an acceleration sensor, were introduced into the master and slave systems through a Chua’s circuit. In a chaotic system, minor differences can cause significant changes that generate dynamic errors. The matter-element model extension can be used to determine the bearing condition. Extension theory can be used to establish classical and sectional domains using the dynamic errors of the fault conditions. The results obtained were compared with those from discrete Fourier transform analysis, wavelet analysis and an integer order chaos system. The diagnostic rate of the fractional-order master and slave chaotic system could reach 100% if the fractional-order parameter adjustment was used. This study presents a very efficient and inexpensive method for monitoring the state of ball bearings.

scholarly journals Soil Salinization Level Monitoring and Classifying by Mixed Chaotic Systems

2021 ◽  
Vol 13 (19) ◽  
pp. 3819
Author(s):  
Anhong Tian ◽  
Chengbiao Fu ◽  
Her-Terng Yau ◽  
Xiao-Yi Su ◽  
Heigang Xiong
Keyword(s):  
Chemical Analysis ◽  
Fractional Order ◽  
Chaotic System ◽  
Classification Accuracy ◽  
Chaotic Dynamic ◽  
Soil Salinization ◽  
Extension Theory ◽  
Non Linear Circuit ◽  
Non Linear ◽  
Dynamic Errors

Soil salinization process is a complex non-linear dynamic evolution. To classify a system with this type of non-linear characteristic, this study proposed a mixed master/slave chaotic system based on Chua’s circuit and a fractional-order Chen-Lee chaotic system to classify soil salinization level. The subject is the soil in Xinjiang with different levels of human interference. A fractional-order Chen-Lee chaotic system was constructed, and the spectral signal processed by the Chua’s non-linear circuit was substituted into the master/slave chaotic system. The chaotic dynamic errors with different fractional orders were calculated. The comparative analysis showed that 0.1-order has the largest chaotic dynamic error change, which produced two distinct and divergent results. Thus, this study converted the chaotic dynamic errors of fractional 0.1-order into chaotic attractors to build an extension matter-element model. Finally, we compared the soil salt contents (SSC) from the laboratory chemical analysis with the results of the extension theory classification. The comparison showed that the combination of fractional order mixed master/slave chaotic system and extension theory has high classification accuracy for soil salinization level. The results of this system match the result of the chemical analysis. The classification accuracy of the calibration set data was 100%, and the classification accuracy of the validation set data was 90%. This method is the first use of the mixed master/slave chaotic system in this field and can satisfy certain soil salinization monitoring needs as well as promote the application of the chaotic system in soil salinization monitoring.

scholarly journals Classifying and Predicting Salinization Level in Arid Area Soil Using a Combination of Chua’s Circuit and Fractional Order Sprott Chaotic System

Sensors ◽  
2019 ◽  
Vol 19 (20) ◽  
pp. 4517 ◽  
Author(s):  
Tian ◽  
Fu ◽  
Su ◽  
Yau ◽  
Xiong
Keyword(s):  
Chemical Analysis ◽  
Fractional Order ◽  
Chaotic System ◽  
Element Model ◽  
Soil Salinization ◽  
Arid Area ◽  
Classification Model ◽  
Human Interference ◽  
Matter Element Model ◽  
Different Levels

Soil salinization is very complex and its evolution is affected by numerous interacting factors produce strong non-linear characteristics. This is the first time fractional order chaos theory has been applied to soil salinization-level classification to decrease uncertainty in salinization assessment, solve fuzzy problems, and analyze the spectrum chaotic features in soil with different levels of salinization. In this study, typical saline soil spectrum data from different human interference areas in Fukang City (Xinjiang) and salt index test data from an indoor chemical analysis laboratory are used as the base information source. First, we explored the correlation between the spectrum reflectance features of soil with different levels of salinization and chaotic dynamic error and chaotic attractor. We discovered that the chaotic status error in the 0.6 order has the greatest change. The 0.6 order chaotic attractors are used to establish the extension matter-element model. The determination equation is built according to the correspondence between section domain and classic domain range to salinization level. Finally, the salt content from the chemical analysis is substituted into the discriminant equation in the extension matter-element model. Analysis found that the accuracy of the discriminant equation is higher. For areas with no human interference, the extension classification can successfully identify nine out of 10 prediction data, which is a 90% identification accuracy rate. For areas with human interference, the extension classification can successfully identify 10 out of 10 prediction data, which is a success rate of 100%. The innovation in this study is the building of a smart classification model that uses a fractional order chaotic system to inversely calculate soil salinization level. This model can accurately classify salinization level and its predictive results can be used to rapidly calculate the temporal and spatial distribution of salinization in arid area/desert soil.

scholarly journals Intelligent Ball Bearing Fault Diagnosis by using Fractional Lorenz Chaos Extension Detection Method with Acceleration Sensor

2018 ◽  
Author(s):  
An-Hong Tian ◽  
Cheng-Biao Fu ◽  
Yu-Chung Li ◽  
Her-Terng Yau
Keyword(s):  
Ball Bearing ◽  
Detection Method ◽  
Low Cost ◽  
Extension Theory ◽  
Acceleration Sensor ◽  
Diagnostic Ratio ◽  
Bearing Fault Diagnosis ◽  
Dynamic Errors ◽  
Chaos System ◽  
Bearing System

In this study we used a non-autonomous Chua’s Circuit, and the fractional Lorenz chaos system together with a detection method from Extension theory to analyze the voltage signals. The measured bearing signals by acceleration sensor were introduced into the master and slave systems through a Chua’s Circuit. In a chaotic system minor differences can cause significant changes that generate dynamic errors, and extension matter-element models can be used to judge the bearing conditions. Extension theory can be used to establish classical and sectional domains using the dynamic errors of the fault conditions. The results obtained were compared with those from Discrete Fourier Transform analysis, Wavelet analysis and an integer order chaos system. The diagnostic ratio showed the fractional order master and slave chaos system calculations. The results show that the method presented in this paper is very suitable for monitoring the operational state of ball bearing system to be superior to the other methods. The diagnosis ratio was better and there were other significant advantages such as low cost and few.

Innovative Intelligent Methodology for the Classification of Soil Salinization Degree Using a Fractional-Order Master-Slave Chaotic System

2019 ◽  
Vol 29 (02) ◽  
pp. 1950026
Author(s):  
An-Hong Tian ◽  
Cheng-Biao Fu ◽  
Hei-Gang Xiong ◽  
Her-Terng Yau
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Phase Plane ◽  
Negative Impact ◽  
Element Model ◽  
Soil Salinization ◽  
System Issue ◽  
Matter Element Model ◽  
Activity Areas

Soil salinization has become a highly significant eco-system issue that is encountered all over the world. Serious soil salinization leads to soil deterioration and has a negative impact on sustainable development of the eco-system and agriculture. However, the spectral reflectance of soils with high overlap and indecipherability makes it difficult to classify the soil salinization degree quickly and accurately. In this paper, an innovative, intelligent methodology using a fractional-order chaotic system to classify the soil salinization degree is proposed. To select a suitable order for the fractional-order chaotic system, the integer-order and noninteger order master-slave Lorenz chaotic systems were used to observe variations in the phase plane distributions. Movement traces of the chaotic system show that severely saline soil will exhibit more active changes, and its distribution status of the Lorenz chaotic system will be more scattered. After analyzing the characteristics of phase plane distributions, a preferred 0.9 fractional-order chaotic system is selected to obtain good analytical characteristics. Finally, extenics theory is used to verify the accuracy of salinization status classified by the coordinate values of the chaotic attractors, and an extenic matter element model is established to analyze the salinization degree. From the results, it was found that 100% analysis accuracy in the judgment of salinization level could be achieved under noninteger order status, and this judgment method is also suitable for soils in different human activity areas. This method has now become a benchmark for testing soil salinization with a chaotic system and is an innovative method that can be used to test the soil salinization degree quickly and accurately.

scholarly journals Amplitude Modulation and Synchronization of Fractional-Order Memristor-Based Chua's Circuit

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
A. G. Radwan ◽  
K. Moaddy ◽  
I. Hashim
Keyword(s):  
Fractional Order ◽  
Amplitude Modulation ◽  
Lyapunov Stability Theory ◽  
Stability And Convergence ◽  
Chua’S Circuit ◽  
Nonlinear Controller ◽  
Chua's Circuit ◽  
Control Functions ◽  
Nonlinear Control Theory ◽  
The Stability

This paper presents a general synchronization technique and an amplitude modulation of chaotic generators. Conventional synchronization and antisynchronization are considered a very narrow subset from the proposed technique where the scale between the output response and the input response can be controlled via control functions and this scale may be either constant (positive, negative) or time dependent. The concept of the proposed technique is based on the nonlinear control theory and Lyapunov stability theory. The nonlinear controller is designed to ensure the stability and convergence of the proposed synchronization scheme. This technique is applied on the synchronization of two identical fractional-order Chua's circuit systems with memristor. Different examples are studied numerically with different system parameters, different orders, and with five alternative cases where the scaling functions are chosen to be positive/negative and constant/dynamic which covers all possible cases from conventional synchronization to the amplitude modulation cases to validate the proposed concept.

A Chemical Chaotic System Derived from Chua's Circuit

2002 ◽  
Vol 2002 (6) ◽  
pp. 295-296
Author(s):  
Wei Guo Xu ◽  
Qian Shu Li
Keyword(s):  
Chaotic System ◽  
Transformation Method ◽  
Nonlinear Transformation ◽  
Mass Action ◽  
Chemical System ◽  
Chua’S Circuit ◽  
Chua's Circuit

Chua's circuit is converted into a mass action chemical system with Samardzija's nonlinear transformation method.

A New Fourth-Order Memristive Chaotic System and Its Generation

2015 ◽  
Vol 25 (11) ◽  
pp. 1550151 ◽  
Author(s):  
Yuxia Li ◽  
Xia Huang ◽  
Yiwen Song ◽  
Jinuan Lin
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponent ◽  
Chaotic System ◽  
Fourth Order ◽  
Bifurcation Analysis ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Diagram Analysis

In this paper, a new fourth-order memristive chaotic system is constructed on the basis of Chua's circuit. Chaotic behaviors are verified through a series of dynamical analyses, including Lyapunov exponent analysis, bifurcation analysis, and phase diagram analysis. In addition, chaos attractors in the newly-proposed system are implemented by hardware circuits.

CHAOTIC DYNAMICS AND SYNCHRONIZATION OF FRACTIONAL-ORDER CHUA'S CIRCUITS WITH A PIECEWISE-LINEAR NONLINEARITY

2005 ◽  
Vol 19 (20) ◽  
pp. 3249-3259 ◽  
Author(s):  
JUN GUO LU
Keyword(s):  
Lyapunov Exponent ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaos Synchronization ◽  
Chaotic Dynamics ◽  
Piecewise Linear ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Synchronization Method ◽  
Simulation Results

In this paper, we numerically investigate the chaotic behaviors of the fractional-order Chua's circuit with a piecewise-linear nonlinearity. We find that chaos exists in the fractional-order Chua's circuit with order less than 3. The lowest order we find to have chaos is 2.7 in the homogeneous fractional-order Chua's circuit and 2.8 in the unhomogeneous fractional-order Chua's circuit. Our results are validated by the existence of a positive Lyapunov exponent. A chaos synchronization method is also presented for synchronizing the homogeneous fractional-order chaotic Chua's systems. The approach, based on stability theory of fractional-order linear systems, is simple and theoretically rigorous. It does not require the computation of the conditional Lyapunov exponents. Simulation results are used to visualize and illustrate the effectiveness of the proposed synchronization method.

Sign in / Sign up

Export Citation Format

Share Document