Method Of False Nearest Neighbors Research Articles

A new fault diagnosis of rolling bearing based on phase-space reconstruction and convolutional neural network

PurposeTo 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.Design/methodology/approachIn 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.FindingsThe 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.Originality/valueThe method proposed in this paper provides a reliable solution in the field of rolling bearing fault diagnosis.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-04-2023-0113/

Estimating a Minimum Embedding Dimension by False Nearest Neighbors Method without an Arbitrary Threshold

Estimating a Minimum Embedding Dimension by False Nearest Neighbors Method without an Arbitrary Threshold

Remaining useful life prediction of lithium-ion batteries based on false nearest neighbors and a hybrid neural network

Accurate estimation of the remaining useful life of lithium-ion batteries is critically important for electronic devices. In the existing literature, the widely applied model-based approaches for remaining useful battery life estimation are limited by the complexity of the electrochemical modeling required. In addition, data-driven approaches for remaining useful battery life estimation commonly define unreliable sliding window sizes empirically and the prediction accuracy of these approaches needs to be improved. To address the above issues, use of a hybrid neural network with the false nearest neighbors method is proposed in this paper. First, the false nearest neighbors method is used to calculate the sliding window size required for prediction. Second, a hybrid neural network that combines the advantages of a convolutional neural network with those of long short-term memory is designed for model training and prediction. Remaining useful life prediction experiments for batteries with various rated capacities are performed to verify the effectiveness of the proposed approach, and the results demonstrate that the proposed approach offers wide generality and reduced errors when compared with the other state-of-the-art methods.

Determining the minimum embedding dimension for state space reconstruction through recurrence networks

The analysis of observed time series from nonlinear systems is usually done by making a time-delay reconstruction to unfold the dynamics on a multi-dimensional state space. An important aspect of the analysis is the choice of the correct embedding dimension. The conventional procedure used for this is either the method of false nearest neighbors or the saturation of some invariant measure, such as, correlation dimension. Here we examine this issue from a complex network perspective and propose a recurrence network based measure to determine the acceptable minimum embedding dimension to be used for such analysis. The measure proposed here is based on the well known Kullback-Leibler divergence commonly used in information theory. We show that the measure is simple and direct to compute and give accurate result for short time series. To show the significance of the measure in the analysis of practical data, we present the analysis of two EEG signals as examples.

On the dimension of complex responses in nonlinear structural vibrations

The ability to accurately model engineering systems under extreme dynamic loads would prove a major breakthrough in many aspects of aerospace, mechanical, and civil engineering. Extreme loads frequently induce both nonlinearities and coupling which increase the complexity of the response and the computational cost of finite element models. Dimension reduction has recently gained traction and promises the ability to distill dynamic responses down to a minimal dimension without sacrificing accuracy. In this context, the dimensionality of a response is related to the number of modes needed in a reduced order model to accurately simulate the response. Thus, an important step is characterizing the dimensionality of complex nonlinear responses of structures.In this work, the dimensionality of the nonlinear response of a post-buckled beam is investigated. Significant detail is dedicated to carefully introducing the experiment, the verification of a finite element model, and the dimensionality estimation algorithm as it is hoped that this system may help serve as a benchmark test case. It is shown that with minor modifications, the method of false nearest neighbors can quantitatively distinguish between the response dimension of various snap-through, non-snap-through, random, and deterministic loads.The state-space dimension of the nonlinear system in question increased from 2–to–10 as the system response moved from simple, low-level harmonic to chaotic snap-through. Beyond the problem studied herein, the techniques developed will serve as a prescriptive guide in developing fast and accurate dimensionally reduced models of nonlinear systems, and eventually as a tool for adaptive dimension-reduction in numerical modeling. The results are especially relevant in the aerospace industry for the design of thin structures such as beams, panels, and shells, which are all capable of spatio-temporally complex dynamic responses that are difficult and computationally expensive to model.

Variable Selection for Nonlinear Soft Sensor Based on False Nearest Neighbors in KICA Space

Selection of secondary variables is an effective way to reduce redundant information and to improve efficiency in nonlinear soft sensor. A novel method based on kernel independent component analysis(KICA) and false nearest neighbors method(FNN) is proposed on selecting the most suitable secondary process variables. The first step is to convert the non-linear operating variables into the linear space with kernel method. One the basis, they are projected into the independent ones with KICA transformations. In order to compare the different impacts on the operating variables, each original variable is eliminated orderly from original datasets with FNN in KICA subspace. In this way, it is possible to trace the important cause for the prediction. The result shows its validity with the verification in hydrocyanic acid(HCN) process industry.

A distributed memory architecture implementation of the False Nearest Neighbors method based on distribution of dimensions

The False Nearest Neighbors (FNN) method is particularly relevant in several fields of science and engineering (medicine, economics, oceanography, biological systems, etc.). In some of these applications, it is important to give results within a reasonable time scale, so the execution time of the FNN method has to be reduced. This paper describes two parallel implementations of the FNN method based on the distribution of embedding dimensions for distributed memory architectures. A "Single-Program, Multiple Data" (SPMD) paradigm is employed using a simple data decomposition approach where each processor runs the same program but acts on a different subset of the data. The computationally intensive part of the method lies mainly in the neighbor search and this task is therefore parallelized and executed using 4 to 64 processors. The accuracy and performance of the two parallel approaches are then assessed and compared to the best sequential implementation of the FNN method which appears in the TISEAN project. The results indicate that the two parallel approaches, when the method is run using 64 processors on the MareNostrum supercomputer, are between 17 and 37 times faster than the sequential one. Efficiency is between 26% and 59%.

Parallel implementations of the False Nearest Neighbors method for distributed memory architectures

AbstractThe False Nearest Neighbors (FNN) method is particularly relevant in several fields of science and engineering (medicine, economics, oceanography, biological systems, etc.). In some of these applications, it is important to give results within a reasonable time scale; hence, the execution time of the FNN method has to be reduced. This paper describes two parallel implementations of the FNN method for distributed memory architectures. A ‘Single‐Program, Multiple Data’ (SPMD) paradigm is employed using a simple data decomposition approach where each processor runs the same program but acts on a different subset of the data. The computationally intensive part of the method lies mainly in the neighbor search and therefore this task is parallelized and executed using 2 to 64 processors. The accuracy and the performance of the two parallel approaches are then assessed and compared with the best sequential implementation of the FNN method, which appears in the TISEAN project. The results indicate that the two parallel approaches, when the method is run using 64 processors on a SGI Origin 3800, are between 40 and 80 times faster than the sequential one. The efficiency is between 65 and 125%. Copyright © 2010 John Wiley & Sons, Ltd.

Analysis of the global warming dynamics from temperature time series

Global warming is the observed increase of the average temperature of the Earth. The primary cause of this phenomenon is the release of the greenhouse gases by burning of fossil fuels, land cleaning, agriculture, among others, leading to the increase of the so-called greenhouse effect. An approach to deal with this important problem is the time series analysis. In this regard, different techniques can be applied to evaluate the global warming dynamics. This kind of analysis allows one to make better predictions increasing our comprehension of the phenomenon. This article applies nonlinear tools to analyze temperature time series establishing state space reconstruction and prediction. Since noise contamination is unavoidable in data acquisition, it is important to employ robust techniques. The method of delay coordinates is employed for state space reconstruction and delay parameters are evaluated using the method of average mutual information and the method of false nearest neighbors. Afterwards, the simple nonlinear prediction method is employed to estimate temperatures of the future. Temperature time series from different places of the planet are used. Initially, the approach is verified considering known parts of the time series and afterwards, results are extrapolated for future values estimating temperature until 2028. Results show that these techniques are interesting to estimate temperature time history, presenting coherent estimations.

Forecasting Volatility in Financial Markets

In this paper, we analyze the stock of Tsingtao Brewery Co Ltd for the 8-year period, from July 31, 2001, to September 11, 2009, a total of 2003 trading days. Using the False Nearest Neighbors method, we obtain the embedding dimension m in the k-nearest neighbour Algorithm. In order to investigate the validity of this method, we apply the modified method to the daily adjusted opening values of the Tsingtao Brewery Co Ltd. We find that the prediction of experimental results is more accurate than traditional methods.

A distributed memory implementation of the False Nearest Neighbors method based on kd-tree applied to electrocardiography

In different fields of science and engineering (medicine, economy, oceanographic, biologic systems, etc) the False Nearest Neighbors (FNN) method has a special relevance. In some of these applications, it is important to provide the results in a reasonable time, thus the execution time of the FNN method has to be reduced. This paper describes a parallel implementation of the FNN method for distributed memory architectures based on k d -tree. A “SingleProgram, Multiple Data” (SPMD) paradigm is employed using a tree decomposition approach where each processor runs the same program but computes a different sub-tree called local tree. As far as the authors know, there is not any parallel implementation of the FNN method based on k d -tree, consisting this implementation the main contribution of the paper. The accuracy and performance of the parallel approach are then assessed and compared to the best sequential kd-tree based implementation of the FNN method, executing from 2 up to 64 processors and running a Lorenz time series and an electrocardiogram signal as case studies. Results are discussed in terms on execution time, speed-up, and efficiency. In terms of speed, our approach was 3∼20 times faster than sequential algorithm.

Parallel implementations of the False Nearest Neighbors method to study the behavior of dynamical models

Dynamical models are an issue of multidisciplinary studies with direct applications in different areas of science and technology (medicine, oceanography, economics, biology, etc.). One way to study dynamical models is through their associated time series in order to find out the model evolution (equilibrium points, orbits, trajectories, etc.) and determine intervals where the predictions are reliable. A key point in this process is the computing of the time series embedding dimension using the False Nearest Neighbors (FNN) method. The FNN method has a high computational cost when long time series are available (or used), so the execution time has to be reduced. This paper describes two parallel implementations of the FNN method for hybrid (shared and distributed) memory architectures. To the best of the authors’ knowledge, the hybrid implementations presented in this paper represent the first parallel implementation of this type. Moreover, considering a hybrid implementation makes it possible to take advantage of different parallel architectures, because knowing the numbers of nodes and the number of cores per node, the software is autotuned in order to exploit the maximum degree of parallelism existing in the target machine. The computationally intensive part of the method lies mainly in the neighbor search and therefore this task is parallelized and executed using 2 to 64 processors. The accuracy and performance of the two parallel approaches are then assessed and compared against the best sequential implementation of the FNN method which appears in the TISEAN project.

Thread-based implementations of the false nearest neighbors method

The False Nearest Neighbors (FNN) method is particularly relevant in different fields of science and engineering (medicine, economy, oceanography, biological systems, etc.). In some of these applications, it is important to give results within a reasonable time scale, so the execution time of the FNN method has to be reduced. This paper describes three parallel implementations of the FNN method for shared memory architectures. The computationally intensive part of the method lies mainly in the neighbors search and therefore this task is parallelized and executed using 2 up 64 processors. The accuracy and performance of the three parallel approaches are then assessed and compared to the best sequential implementation of the FNN method which appears in the TISEAN project. The results indicate that the three parallel approaches, when the method is run using 64 processors on a SGI Origin 3800, are between 25 and 75 times faster than the sequential one. The efficiency is around 35–115%.

Chaotic behaviour of an electrical analogue to the mechanical double pendulum

In this paper the analogy between a mechanical double pendulum and an oscillating electrical system is presented. Instead of using analytic equations, we used the MultiSim circuit simulation environment in order to reproduce and interpret the response of the electrical oscillator. The electrical double pendulum presents a chaotic regime which is studied quantitatively by means of state space reconstruction. For this purpose the optimal delay time is calculated and the minimum embedding dimension is found with the method of False Nearest Neighbors.

Nonlinear Time Series Analysis of Volcanic Tremor Events Recorded at Sangay Volcano, Ecuador

The assumption that volcanic tremor may be generated by deterministic nonlinear source processes is now supported by a number of studies at different volcanoes worldwide that clearly demonstrate the low-dimensional nature of the phenomenon. We applied methods based on the theory of nonlinear dynamics to volcanic tremor events recorded at Sangay volcano, Ecuador in order to obtain more information regarding the physics of their source mechanism. The data were acquired during 21–26 April 1998 and were recorded using a sampling interval of 125 samples s−1 by two broadband seismometers installed near the active vent of the volcano. In a previous study Johnson and Lees (2000) classified the signals into three groups: (1) short duration (<1 min) impulses generated by degassing explosions at the vent; (2) extended degassing ‘chugging’ events with a duration 2–5 min containing well-defined integer overtones (1–5 Hz) and variable higher frequency content; (3) extended degassing events that contain significant energy above 5 Hz. We selected 12 events from groups 2 and 3 for our analysis that had a duration of at least 90 s and high signal-to-noise ratios. The phase space, which describes the evolution of the behavior of a nonlinear system, was reconstructed using the delay embedding theorem suggested by Takens. The delay time used for the reconstruction was chosen after examining the first zero crossing of the autocorrelation function and the first minimum of the Average Mutual Information (AMI) of the data. In most cases it was found that both methods yielded a delay time of 14–18 samples (0.112–0.144 s) for group 2 and 5 samples (0.04 s) for group 3 events. The sufficient embedding dimension was estimated using the false nearest neighbors method which had a value of 4 for events in group 2 and was in the range 5–7 for events in group 3. Based on these embedding parameters it was possible to calculate the correlation dimension of the resulting attractor, as well as the average divergence rate of nearby orbits given by the largest Lyapunov exponent. Events in group 2 exhibited lower values of both the correlation dimension (1.8–2.6) and largest Lyapunov exponent (0.013–0.022) in comparison with the events in group 3 where the values of these quantities were in the range 2.4–3.5 and 0.029–0.043, respectively. Theoretically, a nonlinear oscillation described by the equation +β+γg(x)=fcosωt can generate deterministic signals with characteristics similar to those observed in groups 2 and 3 as the values of the parameters β,γ,f,ω are drifting, causing instability of orbits in the phase space.

NONLINEAR TECHNIQUES TO CHARACTERIZE PRECHATTER AND CHATTER VIBRATIONS IN THE MACHINING OF METALS

In this paper we report on the use of Poincaré sections, phase plane portraits and false nearest neighbor techniques to understand bifurcations in the lathe cutting of aluminum. The experiments presented here offer further evidence of deterministic tool vibrations below the classical onset of chatter. While classical chatter exhibits strong periodic content, these prechatter dynamics exhibit both quasiperiodic and chaotic vibrations. The method of false nearest neighbors predicts an embedding dimenion between 4 and 6 for prechatter cutting conditions while showing a random characteristic for no-cutting running of the machine. A one-dimensional delay-differential equation model is presented which exhibits some of the characteristics of the Poincaré sections of the experimental time series.

Information dimension analysis of chaotic forward volume spin waves in a yttrium–iron–garnet thin film

Forward volume spin waves were excited in a yttrium–iron–garnet film using a microstrip delay line. Low frequency modulations in output power were captured on a digital oscilloscope for various combinations of microwave input frequency and power. Using the decrease in mutual information as a criterion, an embedding delay time was chosen for each time series. The method of false nearest neighbors was then used to calculate a minimal embedding dimension, D. Despite large changes in input frequency (4.4 GHz&amp;lt;f&amp;lt;4.6 GHz) and power (15.7 dBm&amp;lt;P&amp;lt;22.7 dBm), D⩽3 for each time series, indicating a low dimensional system. Finally, the information dimension, d, was estimated by computing the distance from a collection of reference points to their nearest neighbors. The distribution for d was found to be bimodal. When correlated with the input microwave power and frequency, it was found that values of d&amp;lt;2 occurred close to the auto-oscillation threshold in the vicinity of an even dipole gap. d&amp;lt;3 was observed at higher power levels or at frequencies close to an odd dipole gap.

Phase space reconstruction using input-output time series data.

In this paper we suggest that an extension of a procedure recently proposed by Wayland et al. [Phys. Rev. Lett. 70, 580 (1993)] for recognizing determinism in an autonomous time series can also be used as a diagnostic for determining an appropriate embedding dimension for driven ("input-output") systems. We compare the results of this extension to the results produced by the extensions to the method of false nearest neighbors put forward by Rhodes and Morari [Proceedings of the American Control Conference, Seattle, edited by The American Automatic Control Council (IEEE, Piscataway, 1995)] and the method of averaged false nearest neighbors by Cao et al. [Int. J. Bifurcation Chaos 8, 1491 (1998)].

Improving the false nearest neighbors method with graphical analysis.

We introduce a graphical presentation for the false nearest neighbors (FNN) method. In the original method only the percentage of false neighbors is computed without regard to the distribution of neighboring points in the time-delay coordinates. With this presentation it is much easier to distinguish deterministic chaos from noise. The graphical approach also serves as a tool to determine better conditions for detecting low-dimensional chaos, and to get a better understanding on the applicability of the FNN method.

Synchronization of chaos in an array of three lasers

Synchronization of the chaotic intensity fluctuations of three modulated Nd:YAG lasers oriented in a linear array with either a modulated pump or loss is investigated experimentally, numerically, and analytically. Experimentally, synchronization is only seen between the two outer lasers, with little synchrony between outer and inner lasers. Using a false nearest-neighbors method, we numerically estimate the experimental system dynamics to be five dimensional, which is in good agreement with analytical results. Numerically, synchronization is only seen between the two outer lasers, which matches the experimental data well. Lack of synchrony between outer and inner lasers, is explained analytically and then we numerically investigate loss of synchronization of the outer two lasers, observing the occurrence of a blowout bifurcation. Finally, the effects of noise and symmetry breaking are examined and discussed.