STOCHASTIC MODELING AND DIAGNOSTIC CHARACTERISTICS OF TENSION AND VIBROMETRIC SIGNALS FROM TECHNICAL SOURCES VIA DISCRETE WAVELET TRANSFORM
Keywords:
Discrete wavelet, stochastic differential equations, vibration diagnostics, tensometric signal, Bayesian detection, impulse processes.Abstract
Early identification of technical states in complex mechanical systems plays a crucial role in maintaining industrial safety and operational performance. Signals from strain gauges and vibration sensors typically exhibit multiscale, non-stationary, and stochastic traits, posing challenges for reliable detection via traditional spectral techniques. This research develops an advanced mathematical framework for signal diagnostics employing discrete wavelet transformation. The signal is modeled as a generative process within Hilbert space via stochastic differential equations, with impulsive faults represented through Dirac delta functions and jump-diffusion processes. Rigorous theorems validate the wavelet operator's frame properties, energy invariance, and superior impulse localization. Wavelet-domain Neumann-Pearson and Bayesian detectors are derived demonstrating exponential decay in false alarm rates per large deviation theory. Numerical simulations affirm the method's exceptional sensitivity at low signal-to-noise ratios. It establishes a versatile mathematical foundation for predictive maintenance and intelligent industrial monitoring systems.
References
The proposed model shifts signal diagnostics from a global spectral paradigm to a local-stochastic paradigm. The integration of operator theory, statistical detection, and wavelet analysis ensures high accuracy and robustness of the method. This approach provides a promising mathematical foundation for intelligent monitoring systems and predictive maintenance platforms.
