Stochastic Resonance In Bistable System Research Articles

Bearing fault feature extraction based on MOMEDA and CS-Wood–Saxon stochastic resonance

Since rolling bearing is of great significance to ensure the safe and stable operation of rotating machinery, bearing fault feature extraction then demonstrates a hot topic of general interest in industry. In this work, we applied Multipoint Optimal Minimum Entroy Deconvolution Adjusted preprocessing algorithm to deal with the large amount of background noise containing in the collected bearing fault original signal. Then, the Wood–Saxon stochastic resonance nonlinear system model is adopted to solve the bearing fault feature extraction problem, which avoids the frequency interval and system parameters disadvantages in bistable stochastic resonance system. Furthermore, the parameter step and scale transform factor in the Wood–Saxon stochastic resonance nonlinear system is optimized adaptively by Cuckoo Search algorithm, in which way the output signal-to-noise of bearing fault signal is improved significantly. Therefore, the bearing fault feature can be extracted more effectively compared with the classical bistable stochastic resonance system model. Simulation and examples demonstrated that the proposed method can effectively reduce the noise in the signal and enhance the weak feature in bearing fault signal, so as to realize the accurate early bearing fault diagnosis.

Multi frequency weak signals detection based on under-sampling bistable stochastic resonance

Signal detection has a wide range of practical applications. Compared with traditional weak signal detection, the nonlinear effect of noise in the bistable system is typical and easy to extend, so bistable stochastic resonance detection technique has a wider applicability. In this paper, the multi-frequency weak signals detection based on under-sampling bistable stochastic resonance is studied. Based on the theory of bistable stochastic resonance, a simulation model is established to simultaneously detect multiple low-frequency weak signals. The spectrum of input and output signals is obtained through numerical simulation calculation, and the system characteristics are analyzed. When the large parameter signal does not meet the adiabatic approximation theory, the appropriate sampling coefficient can be selected to directly under-sample the input signal to make it conform to the conditions, and then the scale inverse transformation can be carried out. Finally, combined with the simulation analysis, the correctness of the under-sampling bistable stochastic resonance system to detect the multi-frequency weak signals is verified, the sampling rate is reduced, and the complexity is effectively decreased.

Multi-dimensional hybrid potential stochastic resonance and application of bearing fault diagnosis

Stochastic resonance is a method to enhance weak signal by using noise, which has a wide range of applications in weak signal detection. In order to further investigate the application of multi-dimensional coupling stochastic resonance in practical engineering, a Multi-dimensional Double connection coupling Hybrid Potential Stochastic Resonance (MDHPSR) system is proposed in this paper. Firstly, the potential functions of bi-stable and tri-stable are briefly described, and the tri-stable system having a higher output amplitude. Secondly, the effect of different coupling methods on the output of the central and adjacent coupling ends are studied, and the output amplitude of double connection coupling is higher. Then, the double connection coupling of different potential functions is studied, and MDHPSR system effect is the best. Compared with Multi-dimensional Double connection Classical Bi-stable Stochastic Resonance (MDCBSR) system, MDHPSR system has better anti-noise performance. Finally, applying the two multi-dimensional coupling systems to bearing fault diagnosis, MDHPSR system output amplitude is higher and the Signal-to-Noise Ratio (SNR) is improved by more than 3 dB. This demonstrates the superior performance of MDHPSR system for weak signal detection and the value of the multi-dimensional coupling system for practical engineering applications.

Magnetic Anomaly Detection Based on a Compound Tri-Stable Stochastic Resonance System.

In the case of strong background noise, a tri-stable stochastic resonance model has higher noise utilization than a bi-stable stochastic resonance (BSR) model for weak signal detection. However, the problem of severe system parameter coupling in a conventional tri-stable stochastic resonance model leads to difficulty in potential function regulation. In this paper, a new compound tri-stable stochastic resonance (CTSR) model is proposed to address this problem by combining a Gaussian Potential model and the mixed bi-stable model. The weak magnetic anomaly signal detection system consists of the CTSR system and judgment system based on statistical analysis. The system parameters are adjusted by using a quantum genetic algorithm (QGA) to optimize the output signal-to-noise ratio (SNR). The experimental results show that the CTSR system performs better than the traditional tri-stable stochastic resonance (TTSR) system and BSR system. When the input SNR is -8 dB, the detection probability of the CTSR system approaches 80%. Moreover, this detection system not only detects the magnetic anomaly signal but also retains information on the relative motion (heading) of the ferromagnetic target and the magnetic detection device.

A novel image noise reduction method for composite multistable stochastic resonance systems

In the field of digital signal processing, image denoising is an more and more significant research direction. For the traditional noise reduction theory, noise is considered to be harmful, and the image quality can be improved by analyzing noise characteristics and filtering noise. The appearance of stochastic resonance theory proves that noise can be used to enhance signal, which brings new inspiration to image processing. The classical bistable stochastic resonance model has the problems of high potential barrier and easy saturation, which is not conducive to the improvement of image denoising effect. In this paper, a novel type of stochastic resonance potential well model is quoted, which solves the above shortcomings of the bistable stochastic resonance model, and then combines it with the Gaussian model to propose a composite multistable stochastic resonance model. The dynamic principle of the model in signal detection is described, and the influence of system parameters on image noise reduction is analyzed. The whale optimization algorithm is used to optimize the model parameters, and an adaptive compound multistable stochastic resonance system is established to process pictures and measured radar images under different noise backgrounds. The simulation experiment and engineering application show that the model proposed in this paper solves the problem of high potential barrier and easy saturation of the bistable model, and has better image noise reduction ability compared with Wiener filter, median filter, classical bistable stochastic resonance system and novel type of stochastic resonance potential well system.

Time-delayed feedback bistable stochastic resonance system and its application in the estimation of the Polyester Filament Yarn tension in the spinning process

Accurate extraction of natural frequencies of the Polyester Filament Yarn (PFY) vibration can effectively estimate PFY tension. However, due to the special working operating conditions of spinning equipment, the collected PFY vibration signals always contain strong noise components, which severely affect the analysis and processing of those signals. Stochastic resonance has received extensive attention and research in enhancing and extracting feature signals. In this paper, a time-delayed feedback bistable stochastic resonance (TFBSR) system is proposed and the feasibility of the system for natural frequencies extraction is discussed. The potential function, the probability density, the mean first-passage time and the SNR-theory are used to evaluate the TFBSR system. Firstly, through adaptive tuning parameters including barrier parameters, feedback strength, time delay and noise intensity in the TFBSR system, the weak PFY vibration signal, the noise, and the potential can be matched with each other to an extreme, and an optimal output with low-noise interference can be obtained consequently. Secondly, numerical simulation results show that the noise intensity has played an active role in the stochastic resonance effect. Finally, the combination of the TFBSR system and the improved wavelet threshold denoising model is conducive to extracting the natural frequencies of the PFY and making the estimation of the PFY tension in the spinning process. The experimental results indicate that the TFBSR system can accurately extract the natural frequency and improve the energy of the PFY vibration signal under the appropriate system parameters.

A novel two-dimensional exponential potential bi-stable stochastic resonance system and its application in bearing fault diagnosis

It is difficult for classical stochastic resonance systems to extract weak signals under strong noise environment, therefore a novel two-dimensional exponential potential bi-stable stochastic resonance system (NTBSR) is proposed. First, the equivalent potential function, the mean first-pass time (MFPT) and the output signal-to-noise ratio (SNR) of NTBSR are derived under the adiabatic approximation theory. At the same time, the influence of different system parameters on them is explored. Then, NTBSR, the one-dimensional bi-stable stochastic resonance system (OBSR) and the two-dimensional classical bi-stable stochastic resonance system (TCBSR) are respectively simulated numerically, based on the fourth-order Runge–Kutta algorithm. It is found that the output SNR of NTBSR is the best. Finally, the NTBSR is applied to the fault signal diagnosis of different types of bearings, and the parameters are optimized through the adaptive genetic algorithm (AGA). The test results are compared with wavelet transform method, and TCBSR. The detection results on two sets of bearing fault data show that the NTBSR system has better effects on the enhancement and detection of bearing fault signals, and it is verified that the stochastic resonance method is superior to the traditional wavelet transform method in terms of signal detection and noise utilization. This provides good theoretical support and application value for practical engineering application.

Unknown fault diagnosis of planetary gearbox based on optimal rank nonnegative matrix factorization and improved stochastic resonance of bistable system

Unknown fault diagnosis of planetary gearbox based on optimal rank nonnegative matrix factorization and improved stochastic resonance of bistable system

Stochastic resonance in a high-dimensional space coupled bistable system and its application

As a noise-enhanced signal processing method, stochastic resonance has been widely applied in the field of condition detection and fault diagnosis. To further consummate the application of stochastic resonance in practical engineering, a high-dimensional space model based on coupled bistable stochastic resonance system is proposed in this paper. Firstly, taking the three-dimensional space coupled bistable stochastic resonance system as the research object, the influence of system parameters on the output signal-to-noise ratio is analyzed. Then, the output signal-to-noise ratio of the high-dimensional space coupled bistable stochastic resonance system are analyzed in different dimensions. It is found that the output signals of these coupling ends with the same system parameters are identical, and there is always an optimal dimension for a given input so that the output signal-to-noise ratio reaches the maximum. Moreover, simulation results indicate that the proposed model has good feature enhancement ability and anti-noise robustness. Finally, the proposed approach is employed to diagnose fault signals of two different bearing types. The optimal output of the system is determined by establishing the best dimension value. The bigger output signal-to-noise ratio demonstrates that the proposed method outperforms the one-dimensional bistable stochastic resonance and two-dimensional coupled bistable stochastic resonance in weak fault signal detection, which improves the engineering practicability of stochastic resonance theory.

A novel coupled two-dimensional unsaturated asymmetric bistable stochastic resonance system for bearing fault detection

A novel coupled two-dimensional unsaturated asymmetric bistable stochastic resonance (NCTUABSR) method is proposed in this paper, which is formed by coupling a new asymmetric bistable controlled system with a monostable control system, and significantly solves the serious output saturation problem of traditional two-dimensional bistable system. Based on the SPD and MFPT, it is found that with the increase of coupling, the depth and distance of double potential wells in two-dimensional space will decrease, which makes the particles more prone to inter-well transition. Combined with SNR, the performance characteristics of NCTUABSR under the influence of different parameters are deeply analyzed. NCTUABSR is applied to different types of bearings for fault signal detection, and adaptive genetic algorithm is used to optimize the parameters. Compared with different coupling systems, it is found that the detection performance of NCTUABSR has the most advantages, indicating that the system has obvious feasibility in practical engineering applications.

Boosting learning ability of overdamped bistable stochastic resonance system based physical reservoir computing model by time-delayed feedback

Physical reservoir computing (RC), which can be implemented by various physical systems, is a low-cost neuromorphic framework with a fast learning capability. In the previous studies, an overdamped bistable system-based RC (OBRC) inspired by the FitzHugh-Nagumo neuron model has been proposed to construct an outstanding physical RC system. Benefitting from the stochastic resonance effect, the OBRC requires less power and has stronger noise robustness than many conventional physical RC systems. However, compared with conventional physical RC systems, its learning ability is not superior. To boost the performance of the OBRC, we propose an OBRC with time-delayed feedback (TOBRC). In this work, the TOBRC is implemented in a physical setting with time-multiplexing nodes design and simulated on a conventional computer. Moreover, we adopt a powerful optimization algorithm to automatically determine the optimal hyperparameters for both the OBRC and TOBRC; thus, a more precise quantitative discussion on the upper limit of the system can be made. To compare the TOBRC and OBRC, we conducted short-term memory and parity check tasks to assess the short-term memory ability and nonlinearity, which are the two core abilities of physical RC for learning. The results prove that the short-term memory ability and nonlinearity of the proposed TOBRC are 6.46 and 2.15 times higher than those of the OBRC, respectively. Moreover, the TOBRC outperforms the OBRC under different noise conditions. On the MNIST handwritten digit recognition benchmark, the TOBRC exhibited a lower error rate than the OBRC; it was comparable with that of advanced physical RC systems. Our study confirms that the TOBRC can exhibit excellent learning ability in practical problems.

Weak signal enhancement for machinery fault diagnosis based on a novel adaptive multi-parameter unsaturated stochastic resonance

The output saturation problem limits the application of classical bistable stochastic resonance (CBSR) in weak fault diagnosis. Furthermore, the adjustment of system parameters is essential to generate stochastic resonance (SR) for achieving the optimal output. In this paper, a novel adaptive multi-parameter unsaturation bistable stochastic resonance (AMUBSR) system based on piecewise linearization of potential function is proposed. The beetle antennae search (BAS) is adopted to optimize the system parameters, and the output signal-to-noise ratio (SNR) is selected as the objective function. The optimization results of the simulation signal prove that the validity and superiority of BAS algorithm in parameter matching compared with particle swarm optimization (PSO) algorithm and ant colony optimization (ACO) algorithm. Finally, the proposed method obtains the further improvement of the output SNR, higher spectrum peak value at characteristic frequency and bigger recognition quantity than the CBSR method from the diagnosis results of bearing inner ring and outer ring fault signals.

A two-step vibration-sound signal fusion method for weak fault feature detection in rolling bearing systems

The vibration and sound signals get widely applications in fault diagnosis of rolling bearing systems, but the detection accuracy is unstable at different measuring positions. This paper puts forward a two-step vibration-sound signal fusion method, in which sound signal fusion and vibration-sound signal fusion are executed respectively. The sound signals are fused through weighting to the vibration signal to reduce the influence by measuring positions, and the phase difference is eliminated by a sliding window on the time axis. Then a second fusion between the vibration signal and sound signal is conducted after normalization and superposition, and the performance of two-step fusion is compared with the existing direct fusion. Results show that the two-step fusion provides a larger signal-to-noise ratio, and the amplitudes of characteristic frequencies are also higher. A cascaded bistable stochastic resonance system is applied in the post-processing of the fusion signal to make the signal features more clear, and it is proved that the fault detection effect has an obvious improvement after the whole process. This method provides a new approach for weak fault feature detection in vibration and sound signals, and is of great significance for the maintenance of rolling bearing systems.

Weak Feature Extraction of Local Gear Damage Based on Underdamped Asymmetric Periodic Potential Stochastic Resonance

The enhancement of the detection of weak signals against a strong noise background is a key problem in local gear fault diagnosis. Because the periodic impact signal generated by local gear damage is often modulated by high-frequency components, fault information is submerged in its envelope signal when demodulating the fault signal. However, the traditional bistable stochastic resonance (BSR) system cannot accurately match the asymmetric characteristics of the envelope signal because of its symmetrical potential well, which weakens the detection performance for weak faults. In order to overcome this problem, a novel method based on underdamped asymmetric periodic potential stochastic resonance (UAPPSR) is proposed to enhance the weak feature extraction of the local gear damage. The main advantage of this method is that it can better match the characteristics of the envelope signal by using the asymmetry of its potential well in the UAPPSR system and it can effectively enhance the extraction effect of periodic impact signals. Furthermore, the proposed method enjoys a good anti-noise capability and robustness and can strengthen weak fault characteristics under different noise levels. Thirdly, by reasonably adjusting the system parameters of the UAPPSR, the effective detection of input signals with different frequencies can be realized. Numerical simulations and experimental tests are performed on a gear with a local root crack, and the vibration signals are analyzed to validate the effectiveness of the proposed method. The comparison results show that the proposed method possesses a better resonance output effect and is more suitable for weak fault feature extraction under a strong noise background.

Double Gaussian potential stochastic resonance method and its application in centrifugal fan blade crack detection

Stochastic resonance (SR) has been extensively utilized in the field of weak fault signal detection for its characteristic of enhancing weak signals by transferring the noise energy. Aiming at solving the output saturation problem of the classical bistable stochastic resonance (CBSR) system, a double Gaussian potential stochastic resonance (DGSR) system is proposed. Moreover, the output signal-to-noise ratio (SNR) of the DGSR method is derived based on the adiabatic approximation theory to analyze the effect of system parameters on the DGSR method. At the same time, for the purpose of overcoming the drawback that the traditional SNR index needs to know the fault characteristic frequency (FCF), the weighted local signal-to-noise ratio (WLSNR) index is constructed. The DGSR with WLSNR can obtain optimal parameters adaptively, thereby establishing the DGSR system. Ultimately, a DGSR method is proposed and applied in centrifugal fan blade crack detection. Through simulations and experiments, the effectiveness and superiority of the DGSR method are verified.

Low-power-consumption physical reservoir computing model based on overdamped bistable stochastic resonance system

The physical implementation of reservoir computing (RC), a brain-inspired computing framework, is attracting increasing attention in various research fields owing to its capability of quick learning and the relatively simple training process. Although several physical RC models have been envisaged and realized, most of them require additional peripherals; it leads to an increase in the power consumption of the system. In this study, we propose a novel RC model that is based on an overdamped bistable system and exhibits a counter-intuitive phenomenon called stochastic resonance, through which it can transfer noise energy to the information-carrying signal to realize learning with a comparatively low power consumption. The proposed model also possesses the functional capability of filtering and amplification and thus does not require additional peripheral equipment. In order to prove the feasibility and determine the desired operation mode of the system, two basic benchmark tests, namely short-term memory and parity check tasks, were employed to assess the proposed model. The results verify that this work will potentially act as a stepping stone towards realizing even better low-power-consumption physical RC.

A novel underdamped continuous unsaturation bistable stochastic resonance method and its application

In view of the saturation problem of classical bistable stochastic resonance (CBSR) system, an underdamped continuous unsaturation bistable stochastic resonance (UCUBSR) system is investigated and the feasibility of the system for weak fault feature extraction is discussed. Firstly, based on the reason of saturation phenomenon, a new potential function is constructed, which can independently adjust the steepness of the potential walls. The signal to noise ratio (SNR) of the system is derived. Secondly, a modified unsaturation index, amplitude gain, is proposed, and the influence of the steepness on SR based on SNR and amplitude gain is analyzed. The simulation analysis shows that the amplitude gain can be considered as an appropriate index to quantify SR and has a certain compensation effect on the SNR applied to evaluate unsaturation performance. Finally, from the simulation and experiment, a larger amplitude gain indicates that the proposed system has better unsaturation and weak fault detection ability compared with unsaturation bistable stochastic resonance (UBSR), and a higher amplitude of the output signal at the characteristic frequency proves that the amplitude gain as an indicator can further guide the parameter adjustment of SR and facilitate faint fault signature identification.

Research and application of coupled two-dimensional asymmetric bistable stochastic resonance system

Considering that the vibration signal of rolling bearing is very weak and difficult to be extracted under the working environment noise, a two-dimensional asymmetric bistable system (TDAB) is proposed. The system is coupled by two systems, and the weak signal is enhanced by adjusting the control system (monostable system) to adjust the controlled system (asymmetric bistable system). First, under the condition of adiabatic approximation system, the signal-to-noise ratio (SNR) is deduced, and analyzes the influence of different system parameters on the shape of potential function. Then the effects of each parameter on the SNR of the system are analyzed theoretically. Finally, combined with the adaptive intelligent algorithm, the parameters of the controlled system are optimized, and then the coupling coefficient and control system parameters are adjusted to obtain better system performance. The TDAB system obtained is applied to different bearing fault diagnosis and compared with different coupling systems. The experimental results show that the method can extract the characteristic frequency effectively and has good spectrum amplification performance and anti-noise capability. It is proved that the TDAB system can also have good detection effect in practical application.

Piecewise asymmetric exponential potential under-damped bi-stable stochastic resonance and its application in bearing fault diagnosis

It is difficult to extract weak signals in strong noise background, therefore a piecewise asymmetric exponential potential under-damped bi-stable stochastic resonance (PAEUBSR) system is proposed. First, the theoretical analysis of the steady-state probability density (SPD), mean first passage time (MFPT) and output signal-to-noise ratio (SNR) are derived under the adiabatic approximation theory. At the same time, the influence of different system parameters on system performance is explored. Then the PAEUBSR system is applied to the fault signal diagnosis of different types of bearings, and the parameters are optimized through the adaptive genetic algorithm (AGA). The test results are compared with the exponential potential over-damped symmetric bi-stable stochastic resonance (EOSBSR) system and the exponential potential under-damped symmetric bi-stable stochastic resonance (EUSBSR) system. Finally, the detection results on two sets of bearing fault data show that the PAEUBSR system has better effects on the enhancement and detection of bearing fault signals. This provides good theoretical support and application value for this system in subsequent theoretical analysis and practical engineering applications.

Stochastic resonance in cascaded monostable systems with double feedback and its application in rolling bearing fault feature extraction

Stochastic resonance (SR) has been widely concerned and studied in the field of mechanical fault detection due to the capability of weak signal detection. However, research focused on how to improve the performance of SR system and enable it to process large-parameter signals in engineering practice better. Therefore, from the perspective of feedback control and multi-system synergy, this paper presents a double-feedback cascaded monostable SR (CMSR) system and analyzes the SR phenomenon in the system by using the signal-to-noise ratio as the measurement index. It investigates specifically influence of the coefficients on the system performance. Introducing feedback control and serial structure to a monostable system, consisting of a symmetric quartic potential function, not only alters the response characteristics of the monostable system but also significantly improve the system performance. Compared with the classical bistable SR system with low-pass filtering characteristics, the proposed system can exhibit low-pass filtering or band-pass filtering behavior through different combinations of feedback coefficients, which can better match the frequency characteristic of target signal. Finally, the proposed double-feedback CMSR system is used for extraction of the weak signal features in rolling bearing fault detection, and its superiority and feasibility are verified by comparison with other SR systems.