Chaos Time Series Research Articles

Chaos time series vibration analyses of rolling element bearings for failure diagnosis

Chaos time series vibration analyses of rolling element bearings for failure diagnosis

Depth asynchronous time delay reservoir for nonlinear time series forecasting task

The forecasting of nonlinear time series has a wide range of applications both in theoretical research and industrial production, as the fitting of nonlinear systems, the early warning of sunspot activity and the prediction of network traffic peaks in advance. These tasks require models with strong nonlinear mapping capabilities and sufficient short-term memory capacity. Single-node time delay Reservoir (TDR) have been frequently applied on nonlinear time series forecasting tasks. To address the lack of memory capacity of traditional TDR and its extended version (Delay Decoupled Reservoir (DDR), Deep Time-Delay Reservoir (DTDR)), we propose a Depth Asynchronous Time-Delay Reservoir (DATDR) model. Firstly, the model retains the deep network structure of the DTDR to ensure the dynamic properties of the model, and the history states of each layer are from the previous layers instead of the current layer. Secondly, the same signal input method as the DDR is used, i.e., each layer is fed with the original signal, and this data input method ensures that the feature of signal does not decay gradually during the transmission between layers. Finally, a time delay operator is inserted into two adjacent layers, and the memory capacity of the model could be controlled effectively by adjusting the delay time of the time delay operator to accommodate some time series prediction tasks that require long memory capacity. In this paper, eight datasets from three different types are used to validate the proposed model, including NARMA10-30, Mackey-Glass Chaos time series, He ́non map series, Sunspot Sequence, and two real network traffic datasets. Experiments show that proposed model gets significant improvement in memory capacity compared with TDR, DDR, and DTDR, and performs better for some nonlinear time series datasets especially some long-term memory datasets.

Experimental demonstration of channel order recognition in wireless communications by laser chaos time series and confidence intervals

Experimental demonstration of channel order recognition in wireless communications by laser chaos time series and confidence intervals

T-SNE and variational auto-encoder with a bi-LSTM neural network-based model for prediction of gas concentration in a sealed-off area of underground coal mines

A deep learning network is introduced to predict concentrations of gases in the underground coal mine enclosed region using various IoT-enabled gas sensors installed in a metallic gas chamber. The air is sucked automatically at specific intervals from the sealed-off site utilizing a solenoid valve, suction pump, and programmed microprocessor. The gas sensors monitor the gas content in the underground coal mine and communicate gas concentration to the surface server room through a wireless network and cloud storage media. The t-SNE_VAE_bi-LSTM model is proposed in this study as a prediction model that combines the t-SNE, VAE, and bi-LSTM networks. The proposed model's t-SNE method aims to minimize the dimensionality of the recorded gas concentration; and VAE layer intends to retrieve the inner characteristics of low-dimensional gas concentration. Finally, the given model's Bi-LSTM layer tries to forecast the concentrations of CH4, CO2, CO, O2, and H2 gases. The proposed model's prediction accuracy is compared with the existing two models, namely auto-regressive integrated average moving (ARIMA) and chaos time series (CHAOS). The experiment findings demonstrate that the t-SNE_VAE_bi-LSTM model forecasted mean square error (MSE) is more accurate, and it has lesser MSE value of 0.029 and 0.069 for CH4; 0.037 and 0.019 for CO2; 0.092 and 0.92 for CO; 1.881 and 1.892 for O2; and 1.235 and 1.200 for H2 than the ARIMA and CHAOS models, respectively.

Analysis on Effectiveness of Surrogate Data-Based Laser Chaos Decision Maker

The laser chaos decision maker has been demonstrated to enable ultra-high-speed solutions of multiarmed bandit problems or decision-making in the GHz order. However, the underlying mechanisms are not well understood. In this paper, we analyze the chaotic dynamics inherent in experimentally observed laser chaos time series via surrogate data and further accelerate the decision-making performance via parameter optimization. We first evaluate the negative autocorrelation in a chaotic time series and its impact on decision-making detail. Then, we analyze the decision-making ability using three different surrogate chaos time series to examine the underlying mechanism. We clarify that the negative autocorrelation of laser chaos improves decision-making and that the amplitude distribution of the original laser chaos time series is not optimal. Hence, we introduce a new parameter for adjusting the amplitude distribution of the laser chaos to enhance the decision-making performance. This study provides a new insight into exploiting the supremacy of chaotic dynamics in artificially constructed intelligent systems.

Arm order recognition in multi-armed bandit problem with laser chaos time series

By exploiting ultrafast and irregular time series generated by lasers with delayed feedback, we have previously demonstrated a scalable algorithm to solve multi-armed bandit (MAB) problems utilizing the time-division multiplexing of laser chaos time series. Although the algorithm detects the arm with the highest reward expectation, the correct recognition of the order of arms in terms of reward expectations is not achievable. Here, we present an algorithm where the degree of exploration is adaptively controlled based on confidence intervals that represent the estimation accuracy of reward expectations. We have demonstrated numerically that our approach did improve arm order recognition accuracy significantly, along with reduced dependence on reward environments, and the total reward is almost maintained compared with conventional MAB methods. This study applies to sectors where the order information is critical, such as efficient allocation of resources in information and communications technology.

Time Series Prediction Based on Complex-Valued S-System Model

Symbolic regression has been utilized to infer mathematical formulas in order to solve the complex prediction and classification problems. In this paper, complex-valued S-system model (CVSS) is proposed to predict real-valued time series data. In a CVSS model, input variables and rate constants are complex-valued. The time series data need to be translated into complex numbers. The hybrid evolutionary algorithm based on complex-valued restricted additive tree and firefly algorithm is proposed to search the optimal CVSS model. Three financial time series data and Mackey–Glass chaos time series are collected to evaluate our proposed method. The experiment results show that the predicted data are very close to the target ones and our method could obtain the better RMSE, MAP, MAPE, POCID, R2, and ARV performances than ARIMA, radial basis function neural network (RBFNN), flexible neural tree (FNT), ordinary differential equation (ODE), and S-system.

Dynamic channel selection in wireless communications via a multi-armed bandit algorithm using laser chaos time series

Dynamic channel selection is among the most important wireless communication elements in dynamically changing electromagnetic environments wherein, a user can experience improved communication quality by choosing a better channel. Multi-armed bandit (MAB) algorithms are a promising approach that resolve the trade-off between channel exploration and exploitation of enhanced communication quality. Ultrafast solution of MAB problems has been demonstrated by utilizing chaotically oscillating time series generated by semiconductor lasers. In this study, we experimentally demonstrate a MAB algorithm incorporating laser chaos time series in a wireless local area network (WLAN). Autonomous and adaptive dynamic channel selection is successfully demonstrated in an IEEE802.11a-based, four-channel WLAN. Although the laser chaos time series is arranged prior to the WLAN experiments, the results confirm the usefulness of ultrafast chaotic sequences for real wireless applications. In addition, we numerically examine the underlying adaptation mechanism of the significantly simplified MAB algorithm implemented in the present study compared with the previously reported chaos-based decision makers. This study provides a first step toward the application of ultrafast chaotic lasers for future high-performance wireless communication networks.

Generative adversarial network based on chaotic time series

Generative adversarial networks (GANs) are becoming increasingly important in the artificial construction of natural images and related functionalities, wherein two types of networks called generators and discriminators evolve through adversarial mechanisms. Using deep convolutional neural networks and related techniques, high-resolution and highly realistic scenes, human faces, etc. have been generated. GANs generally require large amounts of genuine training data sets, as well as vast amounts of pseudorandom numbers. In this study, we utilized chaotic time series generated experimentally by semiconductor lasers for the latent variables of a GAN, whereby the inherent nature of chaos could be reflected or transformed into the generated output data. We show that the similarity in proximity, which describes the robustness of the generated images with respect to minute changes in the input latent variables, is enhanced, while the versatility overall is not severely degraded. Furthermore, we demonstrate that the surrogate chaos time series eliminates the signature of the generated images that is originally observed corresponding to the negative autocorrelation inherent in the chaos sequence. We also address the effects of utilizing chaotic time series to retrieve images from the trained generator.

Design of type-2 Fuzzy Logic Systems Based on Improved Ant Colony Optimization

An Improved Ant Colony Optimization (IACO) is proposed to design A2-C1 type fuzzy logic system (FLS) in the paper. The design includes parameters adjustment and rules selection, and the performance of the intelligent fuzzy system, which can be improved by choosing the most optimal parameters and reducing the redundant rules. In order to verify the feasibility of the proposed algorithm, the intelligence fuzzy logic systems based on the algorithms are applied to predict the Mackey-Glass chaos time series. The simulations show that both the IACO and ACO have better tracking performances. The results compared with classical algorithm BP ( back-propagation design) shows the tracking performance of IACO is more precise, the result compared with ACO shows that either the training result or the testing result, the tracking performance of IACO is better, and IACO has a faster convergence rate than ACO, the results compared with the Intelligent type-1 fuzzy logic systems show that both the A2-C1 type FLS based on IACO and ACO have better tracking performance than type-1 fuzzy logic system.

Scalable photonic reinforcement learning by time-division multiplexing of laser chaos

Reinforcement learning involves decision-making in dynamic and uncertain environments and constitutes a crucial element of artificial intelligence. In our previous work, we experimentally demonstrated that the ultrafast chaotic oscillatory dynamics of lasers can be used to efficiently solve the two-armed bandit problem, which requires decision-making concerning a class of difficult trade-offs called the exploration–exploitation dilemma. However, only two selections were employed in that research; hence, the scalability of the laser-chaos-based reinforcement learning should be clarified. In this study, we demonstrated a scalable, pipelined principle of resolving the multi-armed bandit problem by introducing time-division multiplexing of chaotically oscillated ultrafast time series. The experimental demonstrations in which bandit problems with up to 64 arms were successfully solved are presented where laser chaos time series significantly outperforms quasiperiodic signals, computer-generated pseudorandom numbers, and coloured noise. Detailed analyses are also provided that include performance comparisons among laser chaos signals generated in different physical conditions, which coincide with the diffusivity inherent in the time series. This study paves the way for ultrafast reinforcement learning by taking advantage of the ultrahigh bandwidths of light wave and practical enabling technologies.

A novel prediction method for down-hole working conditions of the beam pumping unit based on 8-directions chain codes and online sequential extreme learning machine

In the oilfield operation, the beam pumping unit is a very important artificial lift method. As the down-hole parts work at hundred and thousand meters underground, they are hard to be found immediately when failures come out. If we can predict down-hole working conditions and master its continuous operation states in time, great improvement of the oil well production will be developed. In this paper, a novel down-hole working conditions prediction method for the beam pumping unit based on the chaos time series prediction is proposed. First, curve contour of the dynamometer card is redrawn by 8-directions chain codes, and then eight feature vectors are extracted to construct eight feature vector time series; then, the online sequential extreme learning machine (OS-ELM) method is used to build the prediction model, which can realize fast updating with dynamic work condition changes; finally, the grey interval relational degree between the predicted feature vectors and feature vectors of each fault type is calculated to determine the predicted fault type. Actual production data of an oil well are used for example verification, and both online diagnosis and offline diagnosis illustrate the effectiveness of the method.

Short-term data forecasting based on wavelet transformation and chaos theory

A sketch of wavelet transformation and its application was given. Concerning the characteristics of time sequence, Haar wavelet was used to do data reduction. After processing, the effect of “data nail” on forecasting was reduced. Chaos theory was also introduced, a new chaos time series forecasting flow based on wavelet transformation was proposed. The largest Lyapunov exponent was larger than zero from small data sets, it verified the data change behavior still met chaotic behavior. Based on this, chaos time series to forecast short-term change behavior could be used. At last, the example analysis of the price from a real electricity market showed that the forecasting method increased the precision of the forecasting more effectively and steadily.

Comparison between Inverse Model and Chaos Time Series Inverse Model for Long-Term Prediction

This paper presents an inverse model using chaotic behaviour. The chaos time series inverse model, which uses coupling methods between an inverse model and chaos theory can reconstruct a deterministic and low-dimensional phase space by transforming irregular behaviours of nonlinear time-varying systems into a strange attractor (e.g., a Rossler attractor or a Lorenz attractor), and it can then predict future states. For this study, the author used a training dataset measured in an existing high-rise building and examined the predictive abilities of the chaos time series inverse model modelled into phase spaces with strange attractors in comparison with those of the Support Vector Regression (SVR) out of the inverse model. The paper discusses the effective use of the chaos time series inverse model for multi-step ahead prediction.

Chaos time-series prediction based on an improved recursive Levenberg–Marquardt algorithm

An improved recursive Levenberg–Marquardt algorithm (RLM) is proposed to more efficiently train neural networks. The error criterion of the RLM algorithm was modified to reduce the impact of the forgetting factor on the convergence of the algorithm. The remedy to apply the matrix inversion lemma in the RLM algorithm was extended from one row to multiple rows to improve the success rate of the convergence; after that, the adjustment strategy was modified based on the extended remedy. Finally, the performance of this algorithm was tested on two chaotic systems. The results show improved convergence.

Chaos time series prediction based on membrane optimization algorithms.

This paper puts forward a prediction model based on membrane computing optimization algorithm for chaos time series; the model optimizes simultaneously the parameters of phase space reconstruction (τ, m) and least squares support vector machine (LS-SVM) (γ, σ) by using membrane computing optimization algorithm. It is an important basis for spectrum management to predict accurately the change trend of parameters in the electromagnetic environment, which can help decision makers to adopt an optimal action. Then, the model presented in this paper is used to forecast band occupancy rate of frequency modulation (FM) broadcasting band and interphone band. To show the applicability and superiority of the proposed model, this paper will compare the forecast model presented in it with conventional similar models. The experimental results show that whether single-step prediction or multistep prediction, the proposed model performs best based on three error measures, namely, normalized mean square error (NMSE), root mean square error (RMSE), and mean absolute percentage error (MAPE).

504 転動疲労試験における転がり軸受振動のカオス時系列解析(機械力学・計測制御I)

504 転動疲労試験における転がり軸受振動のカオス時系列解析(機械力学・計測制御I)

Prediction for Gas Emission Quantity of the Working Face Based on LSSVM Optimized by Improved Particle Swarm Optimization

Gas emission quantity may forecast the quantity of gas inside the coal, which has important significance for predicting the outburst of gas, but the problem always has not been well solved. Traditional Particle swarm optimization (PSO) algorithm lacks the ability to track the optimal solution while the fitness function changes. An improved algorithm named Time Variant PSO (TVPSO) was proposed to track the optimal solution online. Then it was used to choose the parameters of Least Square Support Vector Machine (LSSVM), which could avoid the man-made blindness and enhance the efficiency of online forecasting. The TVPSO-LSSVM method is based on the minimum structure risk of SVM and the globally optimizing ability of TVPSO to forecast continuously the gas emission quantity of the working face. The method was applied to solve the problem of nonlinear chaos time series prediction. Result shows that the method satisfies the need of online forecasting.

Effect of hybrid circle reservoir injected with wavelet-neurons on performance of echo state network

The Echo State Network (ESN) has attracted wide attention for its superior performance in chaos time-series prediction. However, the complicated ESN topologies and the random reservoirs are difficult to implement in practice. We propose a hybrid circle reservoir (HCR) ESN architecture that comprises the following features: (1) built with low complexity circle reservoir; (2) partly injected with wavelet-neurons; (3) uses fixed connection weights in both input matrix and dynamic reservoir matrix. The HCR model has been successfully applied to solve six application problems, and the results are used to compare with the existing low complexity simple circle reservoir (SCR) ESN. Furthermore, we analyze the performance of the new model under different ratios of wavelet-neurons, different circle distributions and different input sign patterns. Simulation results show that the HCR model achieves significantly better performance in prediction accuracy than the SCR model. Additionally, the HCR model has similar low complexity as the SCR. Moreover, the short-term memory capacity (MC) in the HCR is close to the theoretical optimal MC value.

Chaotic Time Series Adaptive Prediction Based on Volterra Series

At present, the mine has only realized the real-time monitoring of gas, but not the prediction of gas.There were some limitation of the traditional prediction method, such as modeling subjectivism and statistical prediction. Because it can dynamically adjust the parameters of the model, adaptive prediction method can get the current time according to the prediction error of data and the current time, real-time fault prediction model parameters, this is a very consistent with the prediction method for practical use.This paper presents the gas emission chaos time series method by using volterra series prediction, and on the basis to establish time-series prediction models. The results show that the method not only avoids the phase space reconstruction, but also avoid the points in the neighborhood search, in real-time, with very high efficiency.