Time-delayed feedback multistable stochastic resonance in combination with ensemble empirical mode decomposition method and its application in the measurement of the varnished wire tension

The online measurement of varnished wire tension is essential for ensuring production quality. However, weak vibration signals and significant noise interference pose considerable challenges to accurate tension measurement. To address these challenges, this paper proposes a novel method that combines Time-delayed Feedback Multistable Stochastic Resonance (TFMSR) with Ensemble Empirical Mode Decomposition (EEMD) to enhance the weak vibration signals of varnished wire and achieve precise tension measurement. Initially, a time-delay feedback term is incorporated into a multistable stochastic resonance model. By examining the motion of Brownian particles in a potential well, the effects of barrier parameters, feedback strength, delay time, and noise intensity on the stochastic resonance output are analyzed. The results demonstrate that the TFMSR model effectively denoises fault signals and improves the signal-to-noise ratio of the output, thereby providing a solid foundation for extracting the natural frequency of the varnished wire. Subsequently, the proposed TFMSR in combination with the EEMD method is compared to the TFMSR model and traditional signal preprocessing methods for natural frequency extraction. The comparison reveals that the proposed method outperforms the others in accurately identifying the natural frequencies of the varnished wire. Finally, experimental and engineering applications validate the effectiveness and superiority of the TFMSR in combination with the EEMD method for both natural frequency extraction and tension measurement of varnished wire. In summary, the proposed method demonstrates significant advantages in processing weak signals, making it a promising approach for tension measurement in materials such as carbon fibers, polyester fibers, and flexible substrates.