101 results about "Lyapunov exponent" patented technology

The invention relates to a three-order switchable constant Lyapunov exponent spectra chaotic circuit and a using method thereof, wherein, the three-order switchable constant Lyapunov exponent spectrachaotic circuit comprises a single absolute value item chaotic circuit, an attractor adjusting circuit, a double absolute value item chaotic circuit, a phase inverter circuit, an amplitude adjusting circuit and a corresponding switch group; and the method comprises the steps of taking the basic constant Lyapunov exponent spectra chaotic circuit of a single absolute value item as the basis, and utilizing an absolute value arithmetic unit, a linear and nonlinear feedback branch, an adjustable power supply and a switch for constituting the switchable chaotic circuit. A phase track attraction region of the basic constant exponent spectra chaotic circuit is adjusted by switching through the switch and introducing a linear feedback item; the introduction of a nonlinear absolute value item can obtain the constant exponent spectra chaotic circuit with double absolute value items; and the amplitude adjustment of chaotic signals can be realized through the adjustable power supply, and the phasecontrol of the chaotic signals can be realized through the synchronous changes of feedback polarities of a constant item and the absolute value items. The three-order switchable constant Lyapunov exponent spectra chaotic circuit has the advantages of simple circuit, controllable amplitude and phase of the signals and abundant evolution of an attractor, thereby being widely used in chaotic radar, secure communication and fluid stirring.

A method of judging a biological state comprising using: (1) correlation and/or symmetry between Lyapunov exponent and entropy; and/or (2) Higuchi fractal dimension, wherein the Lyapunov exponent, entropy and Higuchi fractal dimension are indices that can express chaotic nature and derived from time series data of biological signals from a subject.

A method for performing computations in a mathematical system which exhibits a positive lyapunov exponent, or exhibits chaotic behavior, comprises varying a parameter of the system. When employed in cryptography, such as, e.g., in a pseudo-random number generator of a stream-cipher algorithm, in a block-cipher system or a HASH/MAC system, unpredictability may be improved. In a similar system, a computational method comprises multiphying two numbers and manipulating at least one of the most significant bits of the number resulting from the multiplication to produce an output. A number derived from a division of two numbers may be used for deriving an output. In a system for generating a sequence of numbers, an array of counters is updated at each computational step, whereby a carry value is added to each counter. Fixed-point arithmetic may be employed. A method of determining an identification value and for concurrently encrypting and/or decrypting a set of data is disclosed.

The invention relates to the technical field of network security evaluation, in particular to a network security situation prediction method based on a combination of the chaos theory and a neural network. The method comprises the following steps: carrying out processing of normalized network security situation value sequence sets through the mutual information method and the cao method to obtain the optimum embedded dimensions of network security situation sample values, carrying out phase-space reconstruction, and analyzing the maximum Lyapunov exponent of reconstructed samples to determine whether the evaluated samples have chaos predictability or not; determining the numbers of nodes of an output layer and a hidden layer of a BPNN according to characteristics of a nonlinear time sequence and experience; carrying out parameter optimization through an improved firefly algorithm, so as to determine network weights and offset values and establish a network security situation prediction model; and inputting test set samples into the BP neutral network for prediction, and carrying out denormalization of obtained prediction values. The method provided by the invention has the advantages that a network security situation can be more precisely predicted, and the network security situation prediction convergence rate can be increased.

The invention discloses a high-resolution synthetic aperture radar (SAR) satellite image speckle de-noising method. Speckle noise statistic characteristics are analyzed, and based on wavelet modulus maximum and Lyapunov exponent theories, useful signals and speckle noise in SAR images are identified by using spatial related processing technology, so when the marginal information is not lost, the speckle noise is greatly attenuated; meanwhile, the 'drift' phenomenon caused by wavelet multi-resolution analysis is corrected, so the de-noising capacity is enhanced and the processing speed is improved; and the method can identify the useful signals and the speckle noise in the SAR images, greatly attenuate the speckle noise when the marginal information is not lost, meanwhile correct the 'drift' phenomenon caused by the wavelet multi-resolution analysis, enhance the de-noising capacity and improve the processing speed.

The invention provides an integrated stabilization chaotic system based PID (Proportion Integration Differentiation) controller optimization control method. The analysis is performed on an integrated stabilization system dynamic model equation to obtain a chaotic system so as to solve the problem of ship stabilization. The chaotic behavior of the system under the certain conditions is verified by a phase diagram and Lyapunov exponent spectrum analysis method, controlled parameters are selected, and the chaotic behavior of the system can be effectively controlled by a nonlinear feedback control method. According to the integrated stabilization chaotic system based PID controller optimization control method, the chaotic dynamics behavior of the system is improved and the original dynamic characteristics of the system are reserved; a chaotic search algorithm is combined with an ant colony algorithm to implement the optimization of the PID control parameters and accordingly the global optimization capability of the ant colony algorithm is high, meanwhile the system convergence speed is improved, and accordingly the control system performance is significantly improved; the value of application to a controller device is high, wherein the ship rolling motion is effectively designed through the controller device.

The invention discloses a chaos-based method for detecting and classifying early single-point faults of a mechanical component. The method comprises the following steps of: processing conventional sample fault signals in different states of the mechanical component to establish check intervals for different fault types; acquiring fault characteristic frequencies corresponding to all single-point fault states of the mechanical component to construct a frequency matrix of a Duffing chaotic oscillator; solving critical thresholds of periodic driving force amplitudes corresponding to different fault characteristic frequencies to construct a frequency-threshold matrix; and finally, adding a signal to be detected to calculate the maximum Lyapunov exponent matrix M, checking according to data inthe M, calculating correlation dimension of the signal to be detected if a fault signal is available, and classifying the faults to determine a fault mode in comparison with the established correlation dimension intervals for different fault types. By adopting the method, the early single-point faults of the mechanical component are detected and classified; and the method has high noise resistance capacity and extremely high fault detection success rate.

The invention provides a method for real-time entering passenger flow volume anomaly detection of an urban rail transit AFC system. First an improved a small data volume method is adopted to calculate Lyapunov exponents of a historical entering passenger flow data time series, the chaotic characteristic of the sequence is verified, then a C-C method is utilized to determine the time delay and optimal embedded dimension of the chaotic time series, phase-space reconstruction is performed on the original time series, a model training test sample set is determined, a large-range grid search method is adopted to optimize model parameters, the optimized model is utilized to predict the entering passenger flow volume of each time period, then the entering amount of each time period in a training sample is utilized to predict the distribution characteristic of a residual series, and finally a confidence interval of entering passenger flow volume predicted residual of each time period at a certain confidence level is determined, thereby determining a threshold upper limit and a threshold lower limit of entering passenger flow volume anomaly detection of a future time period. The method provided by the invention effectively reduces the range of anomaly detection of entering passenger flow volume, and reduces the false alarm rate of data anomaly detection.

The invention discloses a dual-parameter constant-Lyapunov-exponent four-dimensional autonomous super-chaos system. The dual-parameter constant-Lyapunov-exponent four-dimensional autonomous super-chaos system comprises a math model and a realization circuit, and is characterized in that the realization circuit comprises a first channel circuit, a second channel circuit, a third channel circuit and a fourth channel circuit; the first channel circuit, the second channel circuit, the third channel circuit and the fourth channel circuit comprise three operational amplifiers, and auxiliary resistance and capacitor components that can realize four functions of the math model, respectively; and the realization circuit also comprises four analog multipliers used for realizing two quadratic product terms and a cubic product term of the math model. The realization circuit of the invention is simple in structure and convenient for integration, and can greatly promote the development of the chaos system in the technical fields of electronic measuring, weak signal detection, image encryption and privacy communication.

In an apparatus for diagnosing a brain function of a subject 20 by giving a load to a functional site of a living organism of the subject 20, receiving reactions emitted from the living organism of the subject 20 as an electric signal 40, 50, 60 or 70 and analyzing the electric signal 40, 50, 60 or 70, the electric signals 40, 50, 60 an 70 are a voice signal 40, an nystagmus signal 50, a pulse wave signal 60 and a gravity center swinging signal 70. The apparatus selects at least two from among them, calculates chaos theoretical indexes such as Lyapunov exponents according to a chaos theoretical technique, detects changes in the chaos theoretical indexes with passage of time, and collectively evaluates and diagnoses the brain function.

The invention relates to a five-dimensional hyper-chaotic system. With introduction of two non-linear state feedback controllers, the novel five-dimensional hyper-chaotic system is put forward. A chaotic attractor can manifest a two-wing mode and a multi-wing mode in any directions. Because a large positive Lyapunov exponent exists, the chaotic system has complicated dynamics behaviors. Numerical simulation and analysis are performed on basic dynamics characteristics of the system, and discoveries are that the system has a constant Lyapunov exponent characteristic towards certain parameters. The system comprises a reverse proportion circuit, a first integrating circuit, a second integrating circuit, a third integrating circuit, a fourth integrating circuit and a fifth integrating circuit. Output ends of a first operational amplifier, a second operational amplifier, a third operational amplifier, a fourth operational amplifier and a fifth operational amplifier successively output x(x1), y(x2), z(x3), u(x4) and v(x5) which act as three state variables of the hyper-chaotic system. According to the simple five-dimensional hyper-chaotic system, the chaotic attractor of the simple five-dimensional hyper-chaotic system can manifest the two-wing mode or the multi-wing mode in any directions, and the simple five-dimensional hyper-chaotic system is simple in circuit realization so that the system only has three balance points, and has wide application prospects and important application value in the fields of radar, secret communication, electronic countermeasures, etc.

Systems and methods for detecting areas of distinct wind flow in a region of a wind farm are disclosed. Areas of distinct flow can be identified by a computing tool based at least in part on wind velocity field data. For instance, using wind velocity field data, a finite-time Lyapunov exponent (FTLE) field, which measures the rate at which particles are stretching over time relative to each other, can be calculated. The FTLE field can be analyzed to determine the transport barriers in the flow. The maximum transport barriers of the FTLE field describe Lagrangian coherent structures (LCS). The LCS can be used to identify areas of distinct wind flow, which can be used to determine desirable locations for placement of wind measurement data or to identify recirculation zones.

The invention provides a brushless double-feed-motor chaotic analysis method based on the largest Lyapunov exponent. The method is characterized by deriving a non-linear differential equation based on a brushless double-feed-motor d-q shaft mathematic model; taking a reciprocal of a rotor motion time constant as a control parameter of a motor system; according to an actual motor parameter, constructing a chaotic model of a brushless double-feed motor; through calculating the largest Lyapunov exponent of the chaotic model, analyzing a corresponding parameter scope when the motor generates a chaotic phenomenon. Matlab modeling and simulation are used and a parameter condition of the brushless double-feed motor entering into a chaotic motion state is demonstrated.

The invention provides a discrete modeling, stability analysis and parameter design method for a switching converter, and the method is illustrated by taking a single-phase full-bridge inverter and a B00ST converter as examples. The method provided by the invention comprises the steps of solving a state equation in a switching period of the converter by virtue of Matlab to obtain a stroboscopic mapping expression and a numerical solution in an analytical form; and then drawing a bifurcation diagram, a folding diagram, a phase diagram, a Lyapunov exponent spectrum and a Poincare section for performing stability analysis and parameter design on the converter. The modeling, analysis and design processes are finished directly in a time domain. A nonlinear characteristic of the switching converter is reserved in the modeling process, so that the accuracy is higher. The analysis process is finished mainly by utilizing an algorithm of Matlab, so that the manual calculation amount is small and the analysis is simple and convenient. An analysis result can be presented and verified in various forms, and a result of an analytical method can be verified by a result of a numerical method, so that the credibility is ensured.

The invention relates to the technical field of secure communication, in particular to a hyper-chaotic signal generating method and a generating system thereof, wherein the hyper-chaotic signal generating method comprises the following steps: a sinusoidal signal is input to a non-linear circuit which can generate the hyper-chaotic signal, thereby changing the state equation parameter of the non-linear circuit which can generate the hyper-chaotic signal and causing at least two lyapunov indexes of a chaotic system to be larger than 0; the hyper-chaotic signal generating system comprises the non-linear circuit which can generate the hyper-chaotic signal and also comprises a sinusoidal signal generating device connected with a signal input end of the non-linear circuit which can generate the hyper-chaotic signal, and sinusoidal signal generating device outputs the sinusoidal signal to the non-linear circuit which can generate the hyper-chaotic signal, thereby changing the state equation parameter of the non-linear circuit which can generate the hyper-chaotic signal and causing the at least two lyapunov indexes of the chaotic system to be larger than 0.

The invention provides a Lyapunov exponent based power system load prediction method and apparatus. According to the method, a G-P algorithm for correlation dimension calculation, a small data volume method for Lyapunov exponent calculation, and a Euclid formula are improved, and a maximum Lyapunov exponent prediction method is improved by utilizing the three improved methods, so that the prediction precision is further improved and a prediction result is more accurate. According to the apparatus, a modular structure is adopted, so that the apparatus can be conveniently upgraded and maintained. At the same time, a real-time online forecasting apparatus is used for online real-time load data acquisition, online modeling and online forecasting.

The invention discloses a voice endpoint detection method employing a nonlinear feature. The method comprises the following steps: performing preemphasis processing on audio signals; performing framing processing on the audio signals subjected to the preemphasis processing; performing amplitude segmentation on each frame of the audio signals, and calculating a Liapunov exponent of the frame of the audio signals; and comparing the Liapunov exponent of each frame of the audio signals with a set threshold, and determining endpoints of the audio signals. The method provided by the invention better aims at the essence of voice and also provides more accurate information for improving performance of a voice endpoint detection system while reducing the operation complexity. Through correct and effective detection of voice segments, the calculation amount can be reduced, the processing time is shortened, noise interference of effective voice segments can also be eliminated, and subsequent voice processing work and identification performance of the whole system can be greatly improved.

The invention discloses a DDoS (Distributed Denial of Service) attack detection method based on chaos theory analysis, which comprises the following steps: step 1, collecting information network flowdata, and preprocessing the collected flow data; 2, establishing a network normal flow model by adopting a sequence prediction algorithm in the time sequence model; 3, performing subtraction on the network flow normal model and the network flow measurement value to obtain a corresponding new sequence, thereby obtaining an abnormal subsequence of the network flow; 4, analyzing the abnormal subsequence by adopting a Lyapunov exponent in a chaos theory, and judging the state of the system at the current moment. The technical problems that in the prior art, due to the fact that most of attack flows speak from single data, no obvious malicious feature exists, and even a legal normal request appears, the DDoS attack has great difficulty in detection, and at present, there is no effective solution to detect the DDoS attack to eradicate or reduce the brought harm can be solved.

The invention provides a chaos control method of a permanent magnet linear motor based on decoupling and adaptive sliding mode, comprising the following steps: obtaining a motor state equation according to a PMLSM system mathematical model; Constructing chaotic model of permanent magnet linear synchronous motor; The maximum Lyapunov exponent of PMLSM system is calculated under different conditions. The input transformation matrix F and the state feedback matrix K are constructed to decouple the PMLSM system, and the decoupling model of the PMLSM system is obtained. Constructing virtual controlsystem; Adaptive controller is designed according to the virtual control system to control the chaos of PMLSM under the condition that some parameters of PMLSM system are uncertain. The invention provides a chaos control method of a permanent magnet linear motor based on decoupling and adaptive sliding mode, which enables the permanent magnet linear motor to quickly recover from a chaotic runningstate to a stable running state. It has the advantages of strong robustness, fast response speed and high control accuracy.

Systems and methods for predicting the outcome of chaotic systems are described. An example of a prediction system disclosed herein includes, in general, functional elements to vary the initial conditions of a chaotic system and calculate a plurality of possible trajectories for the chaotic system. The prediction system also includes calculating a Lyapunov exponent for each of the plurality of possible trajectories and selecting the trajectory with the smallest Lyapunov exponent as the most likely trajectory to occur.

The invention discloses a Duffing equation-based weak complex signal detection method, which utilizes the parameter sensibility and the noise immunity of the Duffing equation solution to detect the useful signal which is annihilated in the noise. At first, the complex Duffing detection equitation is built, and is then utilized to detect the complex signal, the method comprises the steps that: all the parameters in the equation are determined; the noise variance of the complex signal is estimated, the estimated value is utilized to calculate the gain, wherein e is the expected noise variance of the complex signal to be detected after the gain, the unit is watt, then the complex signal to be detected is multiplied by the gain, so the complex signal to be detected after the gain is obtained; the complex signal g multiplied by cs(t) to be detected after the gain is substituted in the complex Duffing detection equation which is adjusted to the critical state, the solution to the equation is solved, and is utilized to calculate the maximum Lyapunov exponent of the equation; and the output is judged to be detected with useful signal or not according to whether the maximum Lyapunov exponent of the stabilized equation is smaller than 0 or not.

Systems and methods for calculating the Lyapunov exponent of a chaotic system are described. In one particular embodiment, a Lyapunov exponent calculating method includes obtaining a value indicative of a condition of a chaotic system and assigning the value to first and second precision levels, the second precision level having a higher level of precision than the first precision level. The method also includes iterating the chaotic system over time and comparing the value at the first precision level with the value at the second precision level. From the comparison of values at the first and second precision levels, the method calculates the Lyapunov exponent for the chaotic system.

The invention discloses a health assessment method for a diesel engine main bearing, and the method comprises the steps of collecting vibration signals of the main bearing under different faults, and obtaining a visual phase trajectory diagram through phase-space reconstruction and main vector projection; building a deep convolutional neural network model; labeling various fault phase trajectory diagrams, creating a training set, and inputting the training set into the model for learning; when the cross entropy loss function is minimum, stopping iteration, and storing the diagnosis model; on the other hand, collecting vibration signals of various fault main bearings in different health states, calculating and counting the maximum Lyapunov exponent mean value, and using the maximum Lyapunov exponent mean value as a health assessment standard. During evaluation, health evaluation is carried out according to a corresponding health evaluation standard on the basis of a principle of proximity aiming at the fault type. According to the invention, on-line comprehensive monitoring of the service state of the main bearing can be realized, the maintenance mode of the main bearing can be promoted from regular replacement to condition-based maintenance, and the economic benefit can be obviously improved.