Intrinsic Noise Monitoring of Complex Systems

Literature suggests that distinguishing chaos from noise continues to remain a highly contentious issue in the modern age as it has been historically. This is because chaos and noise share common properties which in turn makes it indistinguishable. In this paper, we seek to provide a viable solution to this problem by presenting a novel approach for the differentiating and identifying chaos from noise. The proposed approach is one that is based on dynamical systems, embedding theorem, matrix algebra and statistical theory. To achieve our objective, the distribution, pattern and behaviour of eigenvalues are analysed in-depth. This yields several important properties with broad application, enabling the distinction between chaos and noise in time series analysis. The applicability of the proposed approach is examined using WTI Spot Price time series. Keywords: Chaos; noise; singular value; WTI Spot Price; Hankel matrix; random matrix

Reliable machine condition monitoring and the early detection of faults play an important role in asset management. Information on the condition of machines in a clear, simple form is very valuable for the maintenance and management personnel of the company. This kind of information can be obtained by combining features of vibration signals and the desired number of features from other physical measurements into a dimensionless MIT index. The resulting value gives us information on the condition of the machine. The inverse of MIT index is called the SOL health index. This paper presents the results of investigations concerning the detection of many simultaneous faults using vibration and sound measurements. The signals measured have been processed using real order derivation, and effective features have been calculated from these signals. Based on these features, MIT indices have been calculated, which reliably shows if there are problems with the condition of the machine.

Physical Review E, 2009

Identifying chaos in experimental data-noisy data-remains a challenging problem for which conclusive arguments are still very difficult to provide. In order to avoid problems usually encountered with techniques based on geometrical invariants ͑dimensions, Lyapunov exponent, etc.͒, Poon and Barahona introduced a numerical titration procedure which compares one-step-ahead predictions of linear and nonlinear models ͓Proc. Natl. Acad. Sci. U.S.A. 98, 7107 ͑2001͔͒. We investigate the aformentioned technique in the context of colored noise or other types of nonchaotic behaviors. The main conclusion is that in several examples noise titration fails to distinguish such nonchaotic signals from low-dimensional deterministic chaos.

Mechanical Systems and Signal Processing, 2017

The authors analyse the causes of frequent failures of fixed oil platforms. It has been discovered that noise in the noisy signals received by the sensors of control systems in many cases contains valuable information about the beginning of a platform's transition into the latent period of an emergency state. Considering this specific characteristic, technologies for calculating estimates of the robust correlation functions have been developed. These technologies allow one to determine the noise characteristics and form correlation matrices equivalent to the matrices of the useful signals. Based on these technologies, the authors propose systems for monitoring the beginning of the latent period of the transition of fixed platforms into an emergency state.

2000

A classification of alternative mathematical schemes which determine possible impositions of noise on dynamic systems either of a continuous or a discrete formulation in time is presented. We refer to the results obtained concerning the influence of noise on the correlation dimension and on the largest Lyapunov exponent. A method of constructing models for e€ecting predictions of time series with a finite correlation dimension is presented. Numerical results concerning the influence of various level of additive noise to the Henon attractor are also provided.

Energy Research, 2017

The fault detection of electric machinery is important necessity for stability of system. The noise signal of rotating machinery is utilized for early fault diagnostic. A measured noise signal is divided down by short time duration parts. Fault carrying frequencies are extracted from digitalized signal. Envelope detector and demodulation were utilized for identifying fault frequencies with their harmonics and sidebands. Automated noise analysis is dedicated to detect and report a machinery abnormal condition. Implementation was conducted with noise signals which were obtained from electric motors, turbine generators and bearing fault motors.

Physical Review E, 2002

We focus on classical chaotic systems corrupted by white and colored noise. We study the dependence of the correlation dimension and the Kolmogorov entropy on the noise level and its spectral exponent. As is well known, white noise strongly reduces the width of the scaling region for the correlation dimension and entropy. On the contrary, we demonstrate that colored noise does not basically obscure the scaling region, changing only the shape of the correlation sum for length scales smaller than the noise level. The numerical results show that, even for a noise level as high as ϳ5%, a reasonably wide plateau for the correlation sum is still obtained, but the value of the calculated dimension is somewhat increased. The calculated correlation dimension is a bilinear function of the noise level and the dimension of the noise, which depends on the spectral exponent of the noise. On the other hand, the width of the scaling region for the correlation entropy depends on this spectral exponent, but the value of the plateau does not change substantially.

Springer eBooks, 2022

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Journal of Physics A: Mathematical & Theoretical, 2019

To determine the regular or chaotic nature of the orbits in dynamical systems can be quite an issue. In this article, following Vozikis et al. (2000), we propose a new tool, namely, the Power Spectrum Indicator (PSI), ψ 2 , that enables us to determine, as early as posible, whether an orbit of a two-dimensional map is chaotic or not. This new method is based on the frequency analysis of a data series constucted by recording the logarithm of the amplification factor of the deviation vector of nearby orbits. Accordingly, two datasets are recorded and the χ 2-likelyhood of their power spectra is computed. Ordered orbits have always the same power spectrum, so their χ 2 ≡ ψ 2 acquires a zero value. On the contrary, a chaotic orbit has a power spectrum that varies with time, hence, chaotic orbits always exhibit a non-zero ψ 2 value. Even as regards "sticky" orbits, the PSI method is very effective in the early detection of chaos, while the global behavior of the ψ 2 indicator can provide information (also) on the intense of the chaotic behavior, i.e., on how "strong" or "weak" the associated chaos may be.

IFOST 2017, 2017

Abstrac:In this context proposes a fault detection system based on a noise signal which is obtained through microphone from a electrical machinery. The noise signal of rotating machinery is utilized for early fault diagnostic. Fault detection system with automated noise signal processing consist of: a measured data is divided down by short time duration parts. Fault carrying frequencies are extracted from digitalized signal. Envelope detector and demodulation were utilized for identifying fault frequencies with their harmonics and sidebands. Automated noise analysis is dedicated to detect and report a machinery abnormal condition. Implementation was conducted with noise signals which were obtained from an electric motors, turbine generators and bearing fault motors.