Evolutionary algorithms for the selection of time lags for time series forecasting by fuzzy inference systems

Color Recurrence Plots for Bearing Fault Diagnosis

This paper presents bearing fault diagnosis using the image classification of different fault patterns. Feature extraction for image classification is carried out using a novel approach of Color recurrence plots, which is presented for the first time. Color recurrence plots are created using non-linear embedding of the vibration signals into delay coordinate space with variable time lags. Deep learning-based image classification is then performed by building the database of the extracted features of the bearing vibration signals in the form of Color recurrence plots. A Series of computational experiments are performed to compare the accuracy of bearing fault classification using Color recurrence plots. The standard bearing vibration dataset of Case Western Reserve University is used for those purposes. The paper demonstrates the efficacy and the accuracy of a new and unique approach of scalar time series extraction into two-dimensional Color recurrence plots for bearing fault diagnosis.

General function approximation of a class of cascade chaotic fuzzy systems

This paper presents an innovative architecture called cascade chaotic fuzzy system (CCFS) for the function approximation and chaotic modeling. The proposed model can dominate complications in the type-2 fuzzy systems and increase the chaotic performance of a whole framework. The proposed cascade structure is based on combining two or more one-dimensional chaotic maps. The combination provides a new chaotic map with more high nonlinearity than its grain maps. The fusion of cascade chaotic structure into the neurons of the membership layer of a conventional fuzzy system makes the CCFS more capable of confronting nonlinear problems. Based on the General Function Approximation and Stone-Weierstrass theorem, we show that the proposed model has the function approximation property. By analyzing the bifurcation diagram and applying the CCFS to the problem of chaotic modeling, the new model is investigated. Simulation results and analysis are demonstrated to illustrate the concept of general function approximation.

Interval Type-2 Fuzzy Neural Networks for Chaotic Time Series Prediction: A Concise Overview

Chaotic time series widely exists in nature and society (e.g., meteorology, physics, economics, etc.), which usually exhibits seemingly unpredictable features due to its inherent nonstationary and high complexity. Thankfully, multifarious advanced approaches have been developed to tackle the prediction issues, such as statistical methods, artificial neural networks (ANNs), and support vector machines. Among them, the interval type-2 fuzzy neural network (IT2FNN), which is a synergistic integration of fuzzy logic systems and ANNs, has received wide attention in the field of chaotic time series prediction. This paper begins with the structural features and superiorities of IT2FNN. Moreover, chaotic characters identification and phase-space reconstruction matters for prediction are presented. In addition, we also offer a comprehensive review of state-of-the-art applications of IT2FNN, with an emphasis on chaotic time series prediction and summarize their main contributions as well as some hardware implementations for computation speedup. Finally, this paper trends and extensions of this field, along with an outlook of future challenges are revealed. The primary objective of this paper is to serve as a tutorial or referee for interested researchers to have an overall picture on the current developments and identify their potential research direction to further investigation.

Permutation Entropy Based on Non-Uniform Embedding

A novel visualization scheme for permutation entropy is presented in this paper. The proposed scheme is based on non-uniform attractor embedding of the investigated time series. A single digital image of permutation entropy is produced by averaging all possible plain projections of the permutation entropy measure in the multi-dimensional delay coordinate space. Computational experiments with artificially-generated and real-world time series are used to demonstrate the advantages of the proposed visualization scheme.

Fuzzy Autocorrelation Model with Confidence Intervals of Fuzzy Random Data

Economic analyses are typical methods based on timeseries data or cross-section data. Economic systems are complex because they involve human behaviors and are affected by many factors. When a system includes such uncertainty, as those concerning human behaviors, a fuzzy system approach plays a pivotal role in such analysis. In this paper, we propose a fuzzy autocorrelation model with confidence intervals of fuzzy random timeseries data. These confidence intervals play an essential role in dealing with fuzzy random data on the fuzzy autocorrelation model that we have presented. We analyze tick-by-tick data of stock transactions and compare two time-series models, a fuzzy autocorrelation model proposed by us, and a new fuzzy time-series model that we propose in this paper.

A Novel Time Series Prediction Approach Based on a Hybridization of Least Squares Support Vector Regression and Swarm Intelligence

This research aims at establishing a novel hybrid artificial intelligence (AI) approach, named as firefly-tuned least squares support vector regression for time series prediction(FLSVRTSP). The proposed model utilizes the least squares support vector regression (LS-SVR) as a supervised learning technique to generalize the mapping function between input and output of time series data. In order to optimize the LS-SVR’s tuning parameters, theFLSVRTSPincorporates the firefly algorithm (FA) as the search engine. Consequently, the newly construction model can learn from historical data and carry out prediction autonomously without any prior knowledge in parameter setting. Experimental results and comparison have demonstrated that theFLSVRTSPhas achieved a significant improvement in forecasting accuracy when predicting both artificial and real-world time series data. Hence, the proposed hybrid approach is a promising alternative for assisting decision-makers to better cope with time series prediction.

Optimal Selection of Parameters for Nonuniform Embedding of Chaotic Time Series Using Ant Colony Optimization

The optimal selection of parameters for time-delay embedding is crucial to the analysis and the forecasting of chaotic time series. Although various parameter selection techniques have been developed for conventional uniform embedding methods, the study of parameter selection for nonuniform embedding is progressed at a slow pace. In nonuniform embedding, which enables different dimensions to have different time delays, the selection of time delays for different dimensions presents a difficult optimization problem with combinatorial explosion. To solve this problem efficiently, this paper proposes an ant colony optimization (ACO) approach. Taking advantage of the characteristic of incremental solution construction of the ACO, the proposed ACO for nonuniform embedding (ACO-NE) divides the solution construction procedure into two phases, i.e., selection of embedding dimension and selection of time delays. In this way, both the embedding dimension and the time delays can be optimized, along with the search process of the algorithm. To accelerate search speed, we extract useful information from the original time series to define heuristics to guide the search direction of ants. Three geometry- or model-based criteria are used to test the performance of the algorithm. The optimal embeddings found by the algorithm are also applied in time-series forecasting. Experimental results show that the ACO-NE is able to yield good embedding solutions from both the viewpoints of optimization performance and prediction accuracy.

Optimal reconstruction of dynamical systems: a noise amplification approach

In this work we propose an objective function to guide the search for a state space reconstruction of a dynamical system from a time series of measurements. These statistics can be evaluated on any reconstructed attractor, thereby allowing a direct comparison among different approaches: (uniform or nonuniform) delay vectors, PCA, Legendre coordinates, etc. It can also be used to select the most appropriate parameters of a reconstruction strategy. In the case of delay coordinates this translates into finding the optimal delay time and embedding dimension from the absolute minimum of the advocated cost function. Its definition is based on theoretical arguments on noise amplification, the complexity of the reconstructed attractor, and a direct measure of local stretch which constitutes an irrelevance measure. The proposed method is demonstrated on synthetic and experimental time series.