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A Statistical Chaotic Multifractal Framework for Change-Point Detection and Fault Severity Estimation in Industrial Time Series |
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PP: 1307-1324 |
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doi:10.18576/amis/200515
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Author(s) |
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Fuad S. Al-Duais,
Galal Abdulqader Ahmed Alashaari,
Yasser Mahmoud Aboelmagd,
Ahmed I. Taloba,
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Abstract |
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| Industrial vibration signals can be represented as nonstationary stochastic processes whose dependence structure and scaling behavior evolve during mechanical degradation. This study proposes a statistical chaotic–multifractal framework for fault detection, change-point identification, and severity estimation in industrial time-series signals. The framework combines Multifractal Detrended Fluctuation Analysis (MFDFA) with nonlinear dynamical descriptors to quantify changes in scaling heterogeneity, temporal dependence, dynamical instability, and attractor geometry. Generalized Hurst exponents, mass exponent functions, and multifractal spectra are estimated from successive vibration windows. Phase-space reconstruction is subsequently used to estimate the Largest Lyapunov Exponent and Correlation Dimension. Because these estimators are obtained from dependent and nonstationary observations, their sampling uncertainty is evaluated using moving-block bootstrap confidence intervals. Differences between healthy, intermediate, and near-failure operating states are assessed using resampling-based hypothesis tests, effect sizes, and multiplicity- adjusted significance levels. Rather than combining the extracted measures through an unweighted product, a standardized Chaotic Fractal Spectrum Index (CFSI) is constructed as a statistically estimated linear combination of multifractal spectrum width, Largest Lyapunov Exponent, and Correlation Dimension. Its coefficients are estimated using regularized regression on the training data. A sequential change-point procedure is then applied to the resulting index to identify statistically significant departures from the healthy- state distribution. The framework is evaluated using the NASA IMS bearing run-to-failure vibration dataset. The estimated multifractal spectrum width increases from 0.42 in the healthy state to 1.67 near failure, while the Largest Lyapunov Exponent increases from 0.012 to 0.132 and the Correlation Dimension from 2.10 to 3.89. The estimated CFSI consequently displays a systematic increase with degradation. An out-of-sample power-law severity model achieves an R2 of 0.973, a correlation coefficient of 0.987, an RMSE of 0.028, and an MAE of 0.021. Bootstrap confidence intervals and change-point results provide inferential evidence that the observed increases are associated with fault progression rather than ordinary sampling variability. The proposed framework provides an interpretable statistical representation of degradation dynamics by integrating fractal estimation, uncertainty quantification, hypothesis testing, and sequential fault detection. It therefore offers a mathematically grounded approach to condition monitoring and predictive maintenance in rotating machinery.
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