Chaotic Excitation Research Articles

Fault measurement for SISO system using the chaotic excitation

This work presents an efficient Procedure for fault measurement of the single-input-single-output (SISO) system by driving the system directly with the output of a chaotic oscillator. Firstly, we propose a method to adjust the Lyapunov exponents (LEs) of the chaotic excitation by multiplying each equation with a different acceleration factor. These acceleration factors constitute an acceleration factor field (AFF). Secondly, in order to evaluate the degree of activation to the SISO system, which is excited by the chaotic signal with different acceleration factors, we partition the AFF into fully matched, partially matched and non-matched areas by using the criteria derived from Kaplan–Yorke conjecture. It is proved that chaotic excitation with acceleration factors chosen from the fully matched AFF can sufficiently excite the system, i.e. every change in the eigen-structure of the system will be reflected in the output. Thirdly, attractor based fault feature “prediction error (PE)” and evolutionary algorithm “Backtracking Search Optimization Algorithm (BSA)” is used to find the optimal acceleration factor׳s location in the matched area, then the fault feature is signified by using the chaotic excitation with optimized acceleration factors. Finally, two linear analog circuits with different chaotic excitations are tested to validate the power of the approach. Experiment results show that fully matched chaotic excitation can be used to detect faults in a SISO system, while, non-matched chaotic excitation may be capable of detecting some faults in the system, but there is a risk to make the wrong decision.

Study on chaotic vibration and high vibration intensity of a multi-level partial blocks excitation system

A multi-level partial blocks excitation system was proposed to meet the special requirement of vibration equipment. The dynamic mechanical model was analyzed using Lagrange equations to obtain angular displacement equations of higher level partial block. The instantaneous vibration intensity and amplitude were also found. The simulation test was performed using MATLAB in order to obtain the motion curves, phase-trajectory and Poincare maps of higher level partial block. Due to the fact that the existence of the initial sensitivity, nonrepeatability and complexity of the phase trajectory, and flake points set and many discrete points in Poincare maps, the vibration system exhibited many characteristics of chaotic vibration. It was found that the chaotic excitation system with a strongly nonlinear and wide frequency band could achieve some special exciting vibration properties, such as intermittent high vibration intensity, transient super-high vibration intensity and large vibrating amplitude. Based on these analyses, the vibration mill was developed. The research showed that these measured vibration intensity and amplitude curves were consistent with theoretical analysis and the simulation of the motion curves, phase-trajectory and Poincare maps. In the field of vibration engineering, the special inertial properties are important to overcome work barriers and solve current technological bottlenecks.

Damage identification using chaotic excitation

Vibration-based damage detection methods are popular for structural health monitoring. However, they can only detect fairly large damages. Usually impact pulse, ambient vibrations and sine-wave forces are applied as the excitations. In this paper, we propose the method to use the chaotic excitation to vibrate structures. The attractors built from the output responses are used for the minor damage detection. After the damage is detected, it is further quantified using the Kalman Filter. Simulations are conducted. A 5-story building is subjected to chaotic excitation. The structural responses and related attractors are analyzed. The results show that the attractor distances increase monotonously with the increase of the damage degree. Therefore, damages, including minor damages, can be effectively detected using the proposed approach. With the Kalman Filter, damage which has the stiffness decrease of about 5% or lower can be quantified. The proposed approach will be helpful for detecting and evaluating minor damages at the early stage.

Structural Damage Localization Based on Recurrence Plots of Chaotic Response Attractor

The field of vibration-based structural health monitoring involves extracting a feature which robustly quantifies damage-induced changes of the structural dynamics. Generally, the change of structural characteristics due to damage is analyzed by observing frequencies, mode shapes, damping, etc. However, the change of those modal features due to damage is minor, so that detecting the location of damage is difficult. Recently, an attractor-based monitoring system has been proposed. The recent study using chaotic excitation has demonstrated that the change of the attractor caused by damage is more sensitive than that of the most commonly used frequency and mode shape of the structure, in which the recurrence plot was applied successfully to the damage detection. However, damage localization has not been discussed sufficiently. An attempt in this study was made to develop a damage localization method using chaotic excitation and recurrence quantification analysis. It was demonstrated through experiment results that the proposed system makes it possible to detect damage locations.

Structural Damage Detection of Jointed Frame Structures Using Chaotic Excitation and Attractor Analysis

Engineering assembly structures will suffer joint damage inevitably under environmental loads, which may affect the integrity and functionality of structures, even cause the catastrophic event. In the paper, a method using chaotic excitation and attractor geometrical property analysis to identify the joint damage is investigated. This method utilizes the property that different joint conditions will alter the filtered chaotic signal dimension. Damage features are extracted from reconstructed attractors and used to identify the joint condition. A new parameter based on the attractor local variance is tested as damage feature. An experimental jointed frame structures is designed and the joint damage are induced by varying the fastener preload. The results show that this approach works well for detecting the joint damage and the feature is monotonic varying with the damage increase.

Proposed search forT-odd,P-even interactions in spectra of chaotic atoms

Violation of fundamental symmetries in atoms is the subject of intense experimental and theoretical interest. P-odd, T-even transitions have been observed and are in excellent agreement with electroweak theory. Searches for permanent electric dipole moments have placed bounds on T-odd, P-odd interactions, constraining proposed extensions to the Standard Model of elementary particles. Here we propose a new search for T-odd, P-even (TOPE) interactions in atoms. We consider open-shell atoms, such as the rare-earth atoms, which have dense, chaotic excitation spectra with strong level repulsion. The strength of the level repulsion depends on the underlying symmetries of the atomic Hamiltonian. TOPE interactions lead to enhanced level repulsion. We demonstrate how a statistical analysis of many chaotic spectra can determine the strength of level repulsion; in particular, the variance of the number of levels in an energy range has been shown to be a useful measure. We estimate that, using frequency comb spectroscopy, a sufficient number of chaotic levels could be measured to match or exceed the current experimental bounds on TOPE interactions.

Hyperchaotic probe for damage identification using nonlinear prediction error

The idea of damage assessment based on using a steady-state chaotic excitation and state space embedding, proposed during the recent few years, has led to the development of a computationally feasible health monitoring technique based on comparisons between the geometry of a baseline attractor and a test attractor at some unknown state of health. This study explores an extension to this concept, namely a hyperchaotic excitation. Three different types of Lorenz chaotic/hyperchaotic oscillators are used to provide the excitations and comparisons are made using a prediction error feature called ‘nonlinear auto-prediction error’, which is based on attractor geometry, to evaluate the efficiency of chaotic excitation versus hyperchaotic ones. An 8-degree-of-freedom system and a cantilever beam are two models that are used for numerical simulation. A comparison between the results from the chaotic excitation with the results from each of the hyperchaotic excitations, obtained for both of the numerical models, highlights the higher sensitivity of a hyperchaotic excitation relative to a chaotic excitation. The experimental results also confirm the numerical results conveying the higher sensitivity of the hyperchaotic excitation compared to the chaotic one. A hyperchaotic excitation having three positive Lyapunov exponents is shown in some cases to be even more sensitive than a two-positive-Lyapunov-exponent hyperchaotic excitation.

Optimization of Matched Chaotic Frequency Modulation Excitation Sequences for Multichannel Simultaneously Triggered Ultrasonic Ranging System

The matched spectrum and correlation characteristics are both important to realize the multichannel ultrasonic sensors working together. The spectrum matching can make full use of the bandwidth of the ultrasonic ranging system, and the good correlation characteristic can eliminate crosstalk among multichannel ultrasonic sensors triggering simultaneously. Linear frequency modulation (LFM) excitation sequences have been used as transmission signals for ultrasonic sensors. Due to the narrow bandwidth of the ultrasonic ranging system, the number of available LFM excitation sequences is limited. The chaotic frequency modulation (CFM) excitation sequences, which can generate more available excitation signals, are proposed in this paper. The nondominated sorting genetic algorithm-II is adopted to optimize both the spectrum and correlation characteristic of the CFM excitation sequences. After optimization, the CFM excitation sequences are spectrally matched to the ultrasonic ranging system as well as have best correlation characteristic. Real experiments have been implemented using an ultrasonic ranging system consisting of eight-channel SensComp 600 series electrostatic sensors excited with 2 ms CFM sequences. Experimental results show that spectra of the optimized CFM excitation sequences can match to the system and can work together without crosstalk.

MINOR DAMAGE DETECTION USING CHAOTIC EXCITATION AND RECURRENCE ANALYSIS

In this paper, we propose a new attractor-based structural damage detection technique using chaotic excitation. Attractor is reconstructed using vibration response data and sensitive to the change of the system dynamics. By comparing the change of attractors from healthy and damaged structures, we detect and localize the damage. We use recurrence analysis to analyze the change of attractor. Numerical example demonstrates the robustness and sensitivity of the proposed method.

Detection of system changes due to damage using a tuned hyperchaotic probe

This study explores the use of a hyperchaotic signal as an excitation to probe a system fordynamic changes induced by damage events. In chaotic interrogation a deterministicchaotic input (rather than the more commonly employed stochastic white noise input) isapplied to the structure and the dynamic response is mined for features derived fromits state space reconstruction. The steady-state chaotic excitation is tuned toexcite the structure in a way that optimal sensitivity to dimensionality changes inthe response may be observed, resulting in damage-sensitive features extractedfrom the resulting attractors. The enhanced technique proposed in this paperexplores a hyperchaotic excitation, which is fundamentally new in its use as anexcitation. Hyperchaotic oscillators have at least two Lyapunov exponents, incontrast to simple chaotic oscillators. By using the Kaplan–Yorke conjecture andperforming a parametric investigation, the steady-state hyperchaotic excitation istuned to excite the structure in such a way that the optimal (as will be defined)dimensionality of the steady-state response is achieved. A feature called the ‘averagelocal attractor variance ratio’ (ALAVR), which is based on attractor geometry, isused to compare the geometry of a baseline attractor to a test attractor. Theenhanced technique is applied to analytically and experimentally analyze theresponse of an eight-degree-of-freedom system to the hyperchaotic excitation forthe purpose of damage assessment. A comparison between the results obtainedfrom current hyperchaotic excitation versus a chaotic excitation highlights thehigher damage sensitivity in the system response to the hyperchaotic excitation.

Finite element simulation of the frictional heating of cracks under excitation of intensive ultrasonic waves

A thermo-mechanical coupling finite element (FEM) model is built to simulate frictional heating phenomenon of a crack when the plate containing the crack is excited by intensive ultrasonic waves. In the explicit FEM model, a high-power ultrasonic transducer is included for simulating the phenomena of acoustic chaos, and piezoelectric excitation of the transducer is realized by using a piezoelectric thermal-analogy method. Moreover, the dynamical interaction between both crack faces is modelled by using contact-impact algorithm. In the simulation, Dynamical contact force and relative motion of the crack faces, temperature-rise distribution around the crack, and temperature-rise versus time curves of the crack faces, are quantitatively calculated and analyzed when the plate undergoing chaotic excitation.

Finite element modeling of heating phenomena of cracks excited by high-intensity ultrasonic pulses

A three-dimensional thermo-mechanical coupled finite element model is built up to simulate the phenomena of dynamical contact and frictional heating of crack faces when the plate containing the crack is excited by high-intensity ultrasonic pulses. In the finite element model, the high-power ultrasonic transducer is modeled by using a piezoelectric thermal-analogy method, and the dynamical interaction between both crack faces is modeled using a contact-impact theory. In the simulations, the frictional heating taking place at the crack faces is quantitatively calculated by using finite element thermal-structural coupling analysis, especially, the influences of acoustic chaos to plate vibration and crack heating are calculated and analysed in detail. Meanwhile, the related ultrasonic infrared images are also obtained experimentally, and the theoretical simulation results are in agreement with that of the experiments. The results show that, by using the theoretical method, a good simulation of dynamic interaction and friction heating process of the crack faces under non-chaotic or chaotic sound excitation can be obtained.

Excitation of Chaotic Spin Waves in Magnetic Film Feedback Rings through Three-Wave Nonlinear Interactions

This Letter reports experimental results on the three-wave interactions of backward volume spin waves in a magnetic film and the excitation of chaotic waves through such interactions in a magnetic film-based active feedback ring. The three-wave interactions manifest themselves in the power saturation responses of spin waves, and the chaotic excitation manifests itself in chaotic waveforms and broad spectra. The fractal dimensions of the chaotic signals are finite and can be controlled by changing the ring gain.

The Central Enigma of Consciousness

AbstractAbstract: The nature and physical basis of consciousness remains the central enigma of the scientific description of reality in the third millennium. This paper seeks to examine the phenomenal nature of subjective consciousness and elucidate a possible biophysical basis for its existence, in terms of a form of quantum anticipation based on entangled states driven by chaotic sensitivity of global brain dynamics during decision-making processes. Evidence is presented for the evolutionary emergence of chaotic excitation as a universal sense organ in the founding eucaryotes, which then became used in a context-sensitive manner by complex central nervous systems, leading to the dynamical brain.

The detection of cracks in beams using chaotic excitations

In the field of structural health monitoring (SHM), vibration-based SHM is one of the general approaches to detect and quantify damage to a structural system. Recently, progress has been made by using chaotic excitation signals and attractor-based analysis to detect damage in a structure. In this paper, a new approach for crack detection is explored by means of numerical simulations, using a chaotic signal as an input excitation and attractor-based measures. A cracked beam is modelled as a single degree of freedom piece-wise linear system whose stiffness is different during compression and expansion of the crack. To utilise this feature of the cracked beam, the single-phase portrait of the structural output is divided into two parts corresponding to the compression and expansion of the crack. Then the dissimiliarity between these two halves of the attractor are examined as a function of crack size. The measures introduced in this work are the half-space correlation dimension, which is the correlation dimension measured on one-half of the attractor, and the Hausdorff distance between the two attractors halves. For these two attractor-based measures, their variations are investigated with respect to crack size to find whether they are appropriate crack indicators or not.

Circuit state analysis using chaotic signal excitation

A new testing method for analog circuit is proposed in this paper. A low-pass Butterworth filter is taken as the typical system under test (SUT) since the analog circuits in different types of electronic systems can be regarded as the low-, band- or high-pass active (passive) filters. The chaotic signal, which is generated by an improved Chua's circuit, is employed as the excitation signal of SUT. The SUT is a “narrowband” system compared with the bandwidth of input signal, whose state is analyzed with an error-tracking approach. The experimental result depicts that this testing method can efficiently detect the change of the circuit parameter. Besides, another eight features are extracted from the output signal of SUT for analyzing the SUT states. A discussion is made for comparing the effectiveness of each feature according to the testing results.

Fault diagnosis for analog circuits based on chaotic signal excitation

A fault diagnosis method for analog circuit is proposed in this paper. An all-purpose amplifier is taken as the typical circuit under test (CUT). The chaotic signal, which is generated by an improved Chua's circuit, is employed as the excitation signal of CUT. The algorithm for phase-space reconstruction of chaotic time series is a combination algorithm of multiple autocorrelation and Γ-test. The circuit state is estimated based on detecting the geometric change of Chua's attractor with a data-mining approach. For the purpose of information fusion, another eight features are extracted from the testing data to comprehensively determine the CUT states. A discussion is made for comparing the effectiveness of each feature according to the testing results.

Adaptive parameter identification of servo control systems with noise and high-frequency uncertainties

When identifying the parameters of practical servo systems, the high-frequency system modes are frequently neglected in order to simplify the model. Additionally, avoiding measurement noise in physical experiments is virtually impossible Therefore, selecting an appropriate excitation signal is essential. Specifying white noise, or other such signals, as the input signal may cause the excitation of high-frequency uncertainties, which affects the reliability of the parameter identification process. The current study proposes a novel approach in which a particular class of chaotic signal is employed as the excitation signal in an adaptive parameter identification process. Since chaotic signals typically have stationary, continuous, and band-limited power spectra, they are suitable for on-line parameter identification. The present numerical and experimental results demonstrate that the use of a chaotic excitation signal in the identification process causes the estimated system parameters to converge within identifiable ranges, even when the system includes measurement noise and high-frequency uncertainties. The current results also show that there is good agreement between the dynamics of the real system and those of the estimated model within the operation bandwidth.

Alternans and spiral breakup in a human ventricular tissue model

Ventricular fibrillation (VF) is one of the main causes of death in the Western world. According to one hypothesis, the chaotic excitation dynamics during VF are the result of dynamical instabilities in action potential duration (APD) the occurrence of which requires that the slope of the APD restitution curve exceeds 1. Other factors such as electrotonic coupling and cardiac memory also determine whether these instabilities can develop. In this paper we study the conditions for alternans and spiral breakup in human cardiac tissue. Therefore, we develop a new version of our human ventricular cell model, which is based on recent experimental measurements of human APD restitution and includes a more extensive description of intracellular calcium dynamics. We apply this model to study the conditions for electrical instability in single cells, for reentrant waves in a ring of cells, and for reentry in two-dimensional sheets of ventricular tissue. We show that an important determinant for the onset of instability is the recovery dynamics of the fast sodium current. Slower sodium current recovery leads to longer periods of spiral wave rotation and more gradual conduction velocity restitution, both of which suppress restitution-mediated instability. As a result, maximum restitution slopes considerably exceeding 1 (up to 1.5) may be necessary for electrical instability to occur. Although slopes necessary for the onset of instabilities found in our study exceed 1, they are within the range of experimentally measured slopes. Therefore, we conclude that steep APD restitution-mediated instability is a potential mechanism for VF in the human heart.

20614 カオス状変動圧力を与えた生体時系列信号の分析(非線形)

Results of biological signal analysis of human body subjected to chaotic excitation are presented. Sinusoidal pressure and chaotic pressure are applied to the loins, in reclined position on the bed, respectively. The experiment is then repeated with blood stagnated human body. Electrical signals on the skin are then measured. An electrocardiogram (ECG) is detected from a chest of the body, while electromyogram (EMG) is detected from the muscles of both arms. Pulse sound diagram (PSD) is recorded by using a microphone. Based on time-series of ECG, EMG and PSD, the signals were then analyzed by power spectra and by calculation of their Maximum Lyapunov exponents. It is found that human muscles show influences whether by sinusoidal or chaotic pressure. It is also found that chaotic pressure gives the ECG lower Maximum Lyapunov exponent in both normal and blood-stagnated condition.