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The paper shows that it is possible to reconstruct the dynamical attractors of demand at different levels of the supply chain by using time series duplication and techniques for normalisation. The objective of reconstructing dynamical attractors is to learn more about the long‐term dynamical behaviour of supply chains. Typical patterns that can be encountered through phase space reconstruction are discussed. Based on the analysis of real life supply chains first results are presented on how attractors can be used to better understand the dynamical behaviour of supply chains. The cases show that clear attractors can be identified for consumer and retailer demand. When this demand is compared with supply the phase space analysis becomes an effective tool for identifying distortion in the supply chain. The paper concludes by presenting two examples on how a better understanding of demand attractors have been used to improve operational and tactical planning.

Embedding dimension determination in phase space reconstruction is difficult. The purpose of this paper is to present a new approach for embedding dimension determination based on empirical mode, showing that embedding dimensions for phase space reconstruction could be easily determined according to the number of intrinsic mode functions decomposed by empirical mode decomposition.

Through the relation analysis of intrinsic mode functions and embedding dimensions, the approach for embedding dimension determination by the number of intrinsic mode functions is presented. First, a time series is decomposed into several intrinsic mode functions. Second, correlation analysis between intrinsic mode functions and original signals is investigated, and then false intrinsic mode functions could be eliminated by the analysis of correlation coefficient thresholds, which makes the embedding dimension precise. Finally, the method presented is applied to the Lorenz system, Chen's system, and the Duffing equation. Simulation results prove this method is feasible.

A new approach for embedding dimension determination based on empirical mode decomposition is presented. Compared with G‐P algorithms, this new method is effective and decreases computational complexity.

This method provides an effective qualitative criterion to the selection of embedding dimensions in phase space reconstruction.

This method could be used to determine embedding dimensions of phase space reconstruction and degree‐of‐freedom of nonlinear dynamical systems.

The paper proposes a new method of embedding dimension determination in phase space reconstruction.

To solve the problem that the traditional methods miss key information in the process of bearing fault identification, this paper aims to apply the phase-space reconstruction (PSR) theory and intelligent diagnosis techniques to extend the one-dimensional vibration signal to the high-dimensional phase space to reveal the system information implied in the univariate time series of the vibration signal.

In this paper, a new method based on the PSR technique and convolutional neural network (CNN) is proposed. First, the delay time and the embedding dimension are determined by the C-C method and the false nearest neighbors method, respectively. Through the coordinate delay reconstruction method, the two-dimensional signal is constructed, and this information is saved in a set of gray images. Then, a simple and efficient convolutional network is proposed. Finally, the phase diagrams of different states are used as samples and input into a two-dimensional CNN for learning modeling to construct a PSR-CNN fault diagnosis model.

The proposed PSR-CNN model is tested on two data sets and compared with support vector machine (SVM), k-nearest neighbor (KNN) and Markov transition field methods, and the comparison results showed that the method proposed in this paper has higher accuracy and better generalization performance.

The method proposed in this paper provides a reliable solution in the field of rolling bearing fault diagnosis.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-04-2023-0113/

Nowadays, the breakout of the COVID-19 pandemic has caused an important change in teaching models. The emotional experience of this change has an important impact on online teaching. This paper aims to explore its time evolution characteristics and provide reference for the development of online teaching in the post epidemic era.

The article firstly crawls the online teaching-related comment text data on Zhihu platform and performs emotional calculation to obtain a one-dimensional time series of daily average emotional values. Then, by using non-linear time-series analysis, this paper reconstructs the daily average emotion value time series in high-dimensional phase space, calculates the maximum Lyapunov exponent and correlation dimension and finally, explores the feature patterns through recurrence plot and recurrence quantification analysis.

It was found that the sequence has typical non-linear chaotic characteristics; its correlation dimension indicates that it contains obvious fractal characteristics; the public emotional evolution shows a cyclical rise and fall. By text mining and temporal evolution analysis, this paper explores the evolution law over chronically of the daily average emotion value time series, provides feasible strategies to improve students' online learning experience and quality and continuously optimizes this new teaching model in the era of pandemic.

Based on social knowledge sharing platform of Q&A, this paper models and analyzes users interaction data under online teaching-related topics. This paper explores the evolution law over a long time period of the daily average emotion value time series using text mining and temporal evolution analysis. It then offers workable solutions to enhance the quality and experience of students' online learning, and it continuously improves this new teaching model in the age of pandemics.

The purpose of this study is to analyze the corrosion behavior of 304SS in three kinds of solution, 3.5 per cent NaCl, 5 per cent H₂SO₄ and 1 M (1 mol/L) NaOH, using electrochemical noise.

Corrosion types and rates were characterized by spectrum and time-domain analysis. EN signals were evaluated using a novel method of phase space reconstruction and chaos theory. To evaluate the chaotic characteristics of corrosion systems, the delay time was obtained by the mutual information method and the embedding dimension was obtained by the average false neighbors method.

The varying degrees of chaos in the corrosion systems were indicated by positive largest Lyapunov exponents of the electrochemical potential noise.

The change of correlation dimension in three kinds of solution demonstrated significant differences, clearly differentiating various types of corrosion.

The purpose of this paper is to improve forecasting accuracy for short‐term load series.

A forecasting method based on chaotic time series and optimal diagonal recurrent neural networks (DRNN) is presented. The input of the DRNN is determined by the embedding dimension of the reconstructed phase space, and adaptive dynamic back propagation (DBP) algorithm is used to train the network. The connection weights of the DRNN are optimized via modified genetic algorithms, and the best results of optimization are regarded as initial weights for the network. The new method is applied to predict the actual short‐term load according to its chaotic characteristics, and the forecasting results also validate the feasibility.

For the chaos time series, the hybrid neural genetic method based on phase space reconstruction can carry out the short‐term prediction with the higher accuracy.

The proposed method is not suited to medium and long‐term load forecasting.

The accuracy of the load forecasting is important to the economic and secure operation of power systems; also, the neural genetic method can improve forecasting accuracy.

This paper will help overcome the defects of traditional neural network and make short‐term load forecasting more accurate and fast.

Early fault detection of bearing plays an increasingly important role in the operation of rotating machinery. Based on the properties of early fault signal of bearing, this paper aims to describe a novel hybrid early fault detection method of bearings.

In adaptive variational mode decomposition (AVMD), an adaptive strategy is proposed to select the optimal decomposition level K of variational mode decomposition. Then, a criterion based on envelope entropy is applied to select the optimal intrinsic mode functions (OIMF), which contains most useful fault information. Afterwards, local tangent space alignment (LTSA) is used to denoising of OIMF. The envelope spectrum of the OIMF is used to analyze the fault frequency, thereby detecting the fault. Experiments are conducted in a simulated signal and two experimental vibration signals of bearings to verify the effect of the new method.

The results show that the proposed method yields a good capability of detecting bearing fault at an early stage. The new method can extract more useful information and can reduce noise, which can provide better detection accuracy compared with the other two methods.

An adaptive strategy based on center frequency is proposed to select the optimal decomposition level of variational mode decomposition. Envelope entropy is used to fault feature selection. Combining the advantage of the AVMD-envelope entropy and LTSA, which suits the nature of the early fault signal. So, the proposed method has better detection accuracy, which provides a good alternative for early fault detection of bearings.

This study aims to provide a new method of multiscale directional Lyapunov exponents (MSDLE) calculated based on the state space reconstruction for the nonstationary time series, which can be applied to detect the small target covered by sea clutter.

Reconstructed state space is divided into non-overlapping submatrices whose columns are equal to a predetermined scale. The authors compute eigenvalues and eigenvectors of the covariance matrix of each submatrix and extract the principal components σ_ip and their corresponding eigenvectors. Then, the angles ψ_ip of eigenvectors between two successive submatrices were calculated. The curves of (σ_ip, ψ_ip) reflect the nonlinear dynamics both in kinetic and directional and form a spectrum with multiscale. The fluctuations of (σ_ip, ψ_ip), which are sensitive to the differences of backscatter between sea wave and target, are taken out as the features for the target detection.

The proposed method can reflect the local dynamics of sea clutter and the small target within sea clutter is easily detected. The test on the ice multiparameter imaging X-ban radar data and the comparison to K distribution based method illustrate the effectiveness of the proposed method.

The detection of a small target in sea clutter is a compelling issue, as the conventional statistical models cannot well describe the sea clutter on a larger timescale, and the methods based on statistics usually require the stationary sea clutter. It has been proven that sea clutter is nonlinear, nonstationary or cyclostationary and chaotic. The new method of MSDLE proposed in the paper can effectively and efficiently detect the small target covered by sea clutter, which can be also introduced and applied to military, aerospace and maritime fields.

Online question-and-answer (Q&A) communities serve as important channels for knowledge diffusion. The purpose of this study is to investigate the dynamic development process of online knowledge systems and explore the final or progressive state of system development. By measuring the nonlinear characteristics of knowledge systems from the perspective of complexity science, the authors aim to enrich the perspective and method of the research on the dynamics of knowledge systems, and to deeply understand the behavior rules of knowledge systems.

The authors collected data from the programming-related Q&A site Stack Overflow for a ten-year period (2008–2017) and included 48,373 tags in the analyses. The number of tags is taken as the time series, the correlation dimension and the maximum Lyapunov index are used to examine the chaos of the system and the Volterra series multistep forecast method is used to predict the system state.

There are strange attractors in the system, the whole system is complex but bounded and its evolution is bound to approach a relatively stable range. Empirical analyses indicate that chaos exists in the process of knowledge sharing in this social labeling system, and the period of change over time is about one week.

This study contributes to revealing the evolutionary cycle of knowledge stock in online knowledge systems and further indicates how this dynamic evolution can help in the setting of platform mechanics and resource inputs.

Considering the problem that the high recognition rate of deep learning requires the support of mass data, this study aims to propose an insulating fault identification method based on small data set convolutional neural network (CNN).

Because of the chaotic characteristics of partial discharge (PD) signals, the equivalent transformation of the PD signal of unit power frequency period is carried out by phase space reconstruction to derive the chaotic features. At the same time, geometric, fractal, entropy and time domain features are extracted to increase the volume of feature data. Finally, the combined features are constructed and imported into CNN to complete PD recognition.

The results of the case study show that the proposed method can realize the PD recognition of small data set and make up for the shortcomings of the methods based on CNN. Also, the 1-CNN built in this paper has better recognition performance for four typical insulation faults of cable accessories. The recognition performance is improved by 4.37% and 1.25%, respectively, compared with similar methods based on support vector machine and BPNN.

In this paper, a method of insulation fault recognition based on CNN with small data set is proposed, which can solve the difficulty to realize insulation fault recognition of cable accessories and deep data mining because of insufficient measure data.