Stochastic Resonance Method Research Articles

Low-dose radiographic inspection of welding by a novel aperiodic reverse stochastic resonance method

Abstract Low-dose radiographic inspection is a growing trend in industry to minimize radiation risks to humans and the environment. However, reduction in radiation dose often introduces significant noise, which affects image quality and hinders accurate identification of subtle defects. This study addresses this issue by introducing a novel phenomenon called aperiodic reverse stochastic resonance (ARSR), observed in nonlinear systems excited by aperiodic binary signals. ARSR enables simultaneous amplitude amplification and reversal of signals under specific noise conditions. Leveraging ARSR, we propose an image denoising framework for low-dose radiographic inspections. First, a set of projection data is obtained by using Radon transform to reduce the dimensionality of X-ray images from different angles. Then, the projection data is modulated based on the ARSR system. Finally, the image is reconstructed based on the inverse Radon transform. Simulations and experimental comparison results in welding applications validate the effectiveness of the framework, demonstrating significant improvements in image quality for low-dose radiographic defect detection. Unlike advanced methods such as Gaussian filtering, BM3D, and DnCNN, which operate at the pixel level, ARSR performs denoising at the projection data stage, reducing noise impact, preserving original information, and focusing on physical data processing during imaging. This approach enhances the detection of subtle defects, highlighting the potential of stochastic resonance in image processing.

AEEFCSR: an adaptive ensemble empirical feed-forward cascade stochastic resonance system for weak signal detection

Abstract A novel adaptive ensemble empirical feed-forward cascade stochastic resonance (AEEFCSR) method is proposed in this study for the challenges of detecting target signals from intense background noise. At first, we create an unsaturated piecewise self-adaptive variable-stable potential function to overcome the limitations of traditional potential functions. Subsequently, based on the foundation of a feed-forward cascaded stochastic resonance method, a novel weighted function and system architecture is created, which effectively addresses the issue of low-frequency noise enrichment through ensemble empirical mode decomposition. Lastly, inspired by the spider wasp algorithm and nutcracker optimization algorithm, the spider wasp nutcracker optimization algorithm is proposed to optimize the system parameters and overcome the problem of relying on manual experience. In this paper, to evaluate its performance, the output signal-to-noise ratio (SNR), spectral sub-peak difference, and time-domain recovery capability are used as evaluation metrics. The AEEFCSR method is demonstrated through theoretical analysis. To further illustrate the performance of the AEEFCSR method, Validate the adoption of multiple engineering datasets. The results show that compared with the compared algorithms, the output SNR of the AEEFCSR method is at least 6.2801 dB higher, the spectral subpeak difference is more than 0.25 higher, and the time-domain recovery effect is more excellent. In summary, the AEEFCSR method has great potential for weak signal detection in complex environments.

Fourth-stable stochastic resonance and its application to weak fault signal detection of rotating machinery

Weak characteristic extraction is vital for weak fault signal detection of machinery. Stochastic resonance (SR) is able to transfer noise energy into weak fault characteristic frequency excited by a defect of machines. However, the potential function in SR is vital to enhance weak fault characteristic frequency and determines the capability of SR to improve the signal-to-noise ratio (SNR) of a noisy signal. Now, common potential functions include monostable, bistable and even tri-stable potentials but fourth-stable SR has not been studied and applied to detect early fault characteristic frequency. In this paper, thus, we would investigate the behaviors of SR with a fourth-stable potential subject to additive noise, in which the approximate theoretical expression of the power done by SR is derived to demonstrate the fourth-stable Sr Then, a SR method with the fourth-stable potential is proposed to enhance weak fault characteristic frequency, in which these system parameters are adjusted by using SNR as the objective function and using genetic algorithms adaptively. In this paper, thus, Finally, the proposed method is verified by using a simulated signal with noise and two early fault experiment of rolling element bearings with different levels of defects on the outer and inner races. Moreover, the proposed method is compared with wavelet denoising and fast kurtogram methods. The comparisons indicate that the proposed method has the better performance for enhancing weak fault characteristic frequency or weak useful signals than other two methods and is available to weak fault signal detection of machinery.

Distributed estimation cascade second-order tri-stable stochastic resonance method for random noise suppression in continuous-wave mud pulse telemetry

The extraction of high-quality useful signals in downhole environments has perennially posed a technical challenge for continuous wave mud pulse transmission systems. Traditional denoising methods, such as adaptive filtering and wavelet transform, inevitably compromise the integrity of the original signal's useful components while removing noise. Different from the traditional denoising methods, stochastic resonance (SR) is capable of transferring the energy of noise to the signal, thereby accomplishing the objective of noise suppression. In this paper, based on the second-order tri-stable stochastic resonance detection method combined with the estimation of distribution algorithm (EDA), a distributed estimation cascade second-order tri-stable stochastic resonance (EDA- CSTSR) detection method is proposed for the first time. By constructing 5 groups of simulation signals with different signal-to-noise ratios (SNRs), the denoising performance of distributed estimation CSTSR, Langevin SR, and Duffing SR is analyzed in detail. The results show that compared with Langevin SR and Duffing SR, the EDA-CSTSR can increase the SNR of the input simulation signal by at least 17 dB and significantly increase the amplitude of the useful pulse signal. Moreover, the EDA-CSTSR is applied to process actual data obtained from a drilling site, enabling the recognition of weak signals amidst strong background noise, which highlights the method's excellent practical application value and underscores its potential for further enhancement.

A two-stage Duffing equation-based oscillator and stochastic resonance for mechanical fault diagnosis

Incipient fault-induced weak impulses will not be detected easily using the existing fault extraction methods. Stochastic resonance can flexibly use noises to enhance the signal-to-noise ratio, but it lacks the ability of anti-interference to obtain robustness and reliability fault detection performance. A two-stage method is presented to diagnose faults in mechanical components. The first is to judge the fault existence according to the characteristics of the phase space trajectory diagram of the Duffing oscillator. The second is to employ stochastic resonance method based on the Duffing equation to improve the signal-to-noise ratio of the raw signal, in which the two barrier parameters in the Duffing equation-based bistable system are carefully selected using the artificial bee colony algorithm. In the present two-stage method, the existence of faults and further the fault types in mechanical components are stepwise detected to make full usages of the advantages of Duffing oscillator and Duffing equation-based stochastic resonance method. Numerical simulations and two experimental cases verify the performance of the proposed method for mechanical components fault detection in a strong noise environment.

A new selection method of singular values using correlation coefficients for detecting weak exponential damped sinusoidal signals under strong noise

Weak signal detection has garnered considerable attention in numerous research fields, especially weak signal detection under strong noise, which is an urgent problem researches are concerned with. In this paper, a new criterion to select singular values using correlation coefficients is proposed for detecting weak exponential damped sinusoidal signals. This method has a wide variety of signal processing applications. The innovation of our method lies in selecting the most informative singular values of K rather than the most energetic singular values. The proposed method measures the similarity between component signals and useful signals via the autocorrelation function and correlation coefficient, which can preserve more information of the original signal and be more suitable for weak signal detection scenarios under strong noise. Numerical experiments and analysis are performed to verify the efficiency and effectiveness of our method, and indicate that the presented method is superior to the singular value selection methods based on energy or simple difference principle for correlation coefficients. Compared to stochastic resonance methods suitable for weak signal detection under strong background noise, our proposed method also offer significant advantages. Thus, it is beneficial for theoretical analysis and engineering applications.

Fault diagnosis of rolling bearing based on the three-dimensional coupled periodic potential-induced stochastic resonance

Abstract Conventional bistable and monostable stochastic resonance (SR) methods exhibit certain limitations in their capacity to enhance and extract incipient characteristics. Firstly, the inherent potential function structure, characterized by a singular stable-state paradigm, proves inadequate in accommodating the heterogeneous and multifaceted condition monitoring signals. Secondly, the interconnected dynamic characteristics of the mechanical signals remain unaccounted for. Furthermore, conventional SR methods persist in utilizing a fixed constant as the critical system parameter, thereby neglecting the synergistic interaction among monitoring signals, potential function structures, and scale factors. Owing to the rich dynamic characteristics of the three-dimensional multi-stable coupled periodic potential SR system, it demonstrates superior noise utilization compared to monostable and bistable systems. In view of this, the present formulates a three-dimensional spatial model employing a coupled periodic potential model with nonlinear coupling. Subsequently, a pioneering method for diagnosing rolling bearing faults is introduced, utilizing the framework of three-dimensional multi-stable coupled periodic potential-induced SR. Simulation and experimental results illustrate that this approach effectively enhances and extracts the subtle fault characteristics of rolling bearings, ensuring a clear distinction between the spectral peak at the bearing fault characteristic frequency and the spectral peak originating from the interference noise.

Bearing fault feature extraction method: stochastic resonance-based negative entropy of square envelope spectrum

The early identification of bearing defects has recently attracted increasing attention in the fields of condition monitoring and predictive maintenance because of the critical role of bearings on the reliability and safety of turbomachines. The weak features representing early faults in the vibration signals are often submerged in the environmental noise, which poses a major challenge for the early fault diagnosis of rolling bearings. This study proposes a negative entropy of the square envelope spectrum approach integrated with optimized stochastic resonance (SR)-based signal enhancement for accurate early defect detection of rolling element bearings. The proposed method considers the cyclostationarity and impulsivity of the raw signal, as well as its similarity with the enhanced signal, thus reinforcing the characteristic frequency while integrating the regularity of the raw signal to evaluate the SR performance. A comparison study with different existing methods using both numerical and experimental data was conducted to illustrate the effectiveness and accuracy of the proposed methodology for early defect detection of rolling element bearings in different locations. The results show that the proposed method improves the fault detection by 3.5 d earlier than other SR methods, and produces the best enhancement results for fault detection in the outer race, inner race, and rolling element of bearings, with the increase of characteristic frequency intensity coefficient by 126.3%, 118.1%, and 100.5% compared to traditional envelope signals, respectively.

Fault diagnosis of needle selector drive parts based on adaptive stochastic resonance with improved generative adversarial networks

Piezoelectric needle selectors, as key weaving components in the jacquard knitting process of knitting machinery, are widely used in textile equipment. Accurate diagnostic procedures for needle selector drive faults are crucial to ensure the normal operation of the equipment. However, traditional vibration diagnosis methods cannot detect weak periodic signals, resulting in low accuracy of monitoring results. To address this issue, this paper proposes an adaptive stochastic resonance (SR) method based on an improved generative adversarial network (IGAN). Firstly, in order to solve the problem of difficulty in obtaining stochastic resonance parameters, SR is combined with IGAN, and IGAN provides the optimal SR parameters. Secondly, a soft threshold residual attention mechanism and residual network were introduced in the GAN network, and multiple generators were utilized to alleviate the problem of model collapse, in order to adapt to the actual working environment. In addition, due to the large amount of data, it is recommended to use feature parameters for training to improve the efficiency of model training. Finally, through a typical vibration data, the influence of different parameter quantities on the training accuracy of the model was studied, and the superiority of the proposed model compared to other models and the stability of the model under different environmental influences were explored. The results show that this method can effectively detect weak periodic signals of the needle selection driver, effectively alleviate the problem of model collapse in different environments, and is superior to existing methods in terms of accuracy and stability.

Fault feature extraction method of rolling bearings based on coupled resonance system with vibrational resonance-assisted enhanced stochastic resonance

Stochastic resonance (SR), as a signal processing method that is able to use noise to enhance weak periodic signals, provides effective technical support for the detection of weak signals. However, due to the constraints of potential functions or control means, the detection results of a single SR system on weak signals often fails to achieve the desired effect. Through the interaction between different subsystems, SR under the action of multiple systems can obtain rich dynamic response characteristics and improve the detection ability of weak signals. Therefore, this paper proposes a fault feature extraction method of rolling bearings based on a coupled resonance system with vibrational resonance (VR)-assisted enhanced SR. First, a SR system based on a matched steady-state potential model is constructed, which has the ability to alleviate the phenomenon of output saturation to some extent compared with the classical bistable SR. Second, inspired by the synergy of multiple systems, a coupled resonance system with VR-assisted enhanced SR is constructed by combining VR control and SR control, which has the dual advantages of VR and SR and performs well in weak signal detection. Finally, simulation experiment and fault data of rolling bearings are adopted to analyze the suggested method, and the comparison results with other SR methods verify its practicality and superiority.

Periodicity-assist double delay-controlled stochastic resonance for the fault detection of bearings

This paper analyses the stochastic resonance of a double delay-controlled nonlinear system based on the high-order-degradation potential function. It provides a theoretical derivation of the stationary probability density, mean first-passage time (MFPT), and signal-to-noise ratio (SNR), while the marginal probability density is examined via Monte-Carlo simulation. In the field of fault detection for faulty bearings, the stochastic resonance of the nonlinear system encounters a challenge where the exact fault period must be known beforehand. Unfortunately, it is not available for the real engineering application. Consequently, this paper proposes the periodicity-assisted stochastic resonance method, which uses the blind deconvolution technique. The proposed method allows for adaptive determination of the fault frequency from the vibration signal and successfully enhances the power of the signal component corresponding to the determined fault frequency. Compared with the state-of-the-art methods, the proposed method shows better performance, which is validated by the simulated and experimental data. Overall, the proposed method is advantageous for enhancing the weak fault characteristic which is interfered by the strong noise and random impulses.

A stochastic resonance etection algorithm based on orthonormalized basis function for magnetic anomaly detection.

To address the problem that the performance of the detector in airborne magnetic anomaly detection (MAD) is terrible, a stochastic resonance (SR) detection algorithm based on orthonormalized basis function (OBF-SR) is proposed for MAD under low signal-to-noise ratio conditions. The signal contaminated by noise is first preprocessed by the OBF method, where the sum of the three components in the OBF space is selected as the SR system input. Then, a parallel SR system with different initial states is designed to detect the signal. Finally, the simulation analysis of MAD methods is performed to draw a comparison between the OBF-SR method, the typical SR method, and the OBF method. The results show that the OBF-SR method outperforms the SR and OBF methods in the detection probability and detection range under the same conditions.

Single acoustic vector sensor DOA enhanced by unsaturated bistable stochastic resonance with linear amplitude response constrained

Acoustic vector sensors (AVS) are increasingly utilized for remote target passive perception, but accurate direction-of-arrival (DOA) estimation remains a formidable challenge, particularly in the presence of heavy background noise. In this paper, we propose a novel DOA estimation method that utilizes complex acoustic intensity measurements (CAIM) and unsaturated bistable stochastic resonance with linear amplitude response constrained (LAR-UBSR). The proposed method aims to exploit the excellent denoising performance of stochastic resonance (SR) to enhance the accuracy of DOA estimation. The proposed LAR-UBSR method is based on the theoretical analysis of the signal pre-processing requirements of CAIM, which determines the linear amplitude response and fixed phase shift. LAR-UBSR achieves a stable phase shift and linear amplitude response by utilizing the unsaturated potential well and limited potential parameters adjustment method of SR. We analyze the amplitude response linearity of LAR-UBSR under different signal-to-noise ratios (SNRs) and a wide range of frequencies, demonstrating a larger linear amplitude response interval that meets the signal pre-processing requirements of CAIM. Numerical analysis and application verification show that the proposed DOA method outperforms existing methods, particularly under low SNR conditions. The results suggest the potential for high-accuracy DOA estimation using nonlinear signal processing strategies in the presence of heavy background noise.

Feed-forward cascaded stochastic resonance and its application in ship radiated line signature extraction

Extracting ship-radiated line signatures from intense background noise presents a significant challenge in remote passive sonar detection and identification. While stochastic resonance (SR) has shown promise for enhancing signal-to-noise ratio (SNR), cascaded stochastic resonance (CSR) offers a superior extension by gradually transitioning energy from high to low frequencies, resulting in smoother waveforms and more evident signatures. However, CSR relies heavily on the first level and lacks robustness, especially at slightly lower SNR. To overcome these limitations, we propose a feed-forward cascaded stochastic resonance (FCSR) method that leverages complete target signal information in each level and superimposes it with the output from the last level, leading to gradual improvements in SNR with high robustness. The superposition weights are designed as a function of the number of cascaded levels with an increasing trend to optimize the output of the entire cascaded system. Furthermore, a phase alignment strategy was developed to improve the superposition process. Through theoretical analysis, we demonstrate the effectiveness of the proposed FCSR method. Further simulation analyses demonstrates that FCSR outperforms CSR, with a remarkable 18 dB improvement in filtering performance under low SNR conditions, an average anti-noise ability enhancement of over 10 dB, and a robustness improvement exceeding 30% at −30 dB. We also validate the practicality and effectiveness of our proposed method through application verification, exhibiting excellent enhancement performance. This study illuminates the importance of reutilizing complete target signal information and emphasizes the potential of cascaded systems to extract signatures from heavy background noise.

A novel adaptive weak fault diagnosis method based on modulation periodic stochastic pooling networks

Stochastic resonance, known for its strong capability to amplify weak signals, has been widely applied in rotating machinery fault diagnosis. However, the increasing intelligence of mechanical equipment and the harsh service environment leads to new challenges for stochastic resonance method. Moreover, the adaptive stochastic resonance system relying on the signal-to-noise ratio (SNR) as the loss function requires extensive prior knowledge of the signal to be measured, limiting its application in engineering. Therefore, this paper presents a modulation periodic stochastic pooling networks (MPSPN) with integral modulation factor. By using the normalized least-mean-square (NLMS)algorithm, an adaptive bearing fault diagnosis method based on MPSPN under unknown faults is developed. The study first proposes a modulated periodic stochastic resonance (MPSR) model and investigates its stochastic resonance characteristics through the steady-state probability density. Then, it introduces a modulation signal detection index (IMBF) and derives an adaptive weight allocation scheme under NLMS optimization. Finally, the superiority of the MPSPN system is demonstrated through simulations and the analysis of bearing fault data obtained from two distinct experimental platforms. The results indicate that, in comparison to the conventional periodic stochastic resonance (PSR) system, the MPSPN system is capable of effectively diagnosing unknown faults in bearings and significantly improving the SNR of the diagnostic output.

Coupled Hybrid Stochastic Resonance With Multiobjective Optimization for Machinery Dynamic Signature and Fault Diagnosis

Most traditional stochastic resonance methods pose three fundamental limitations in extracting fault signature: (1) simulated impulse signals are insufficient to match the complicated mechanical vibration signals; (2) one-dimensional signals are vulnerable to interference from multiscale noise, which potentially yields false detection; and (3) optimization function in the signal-to-noise ratio largely depends on the advanced requirements of the characteristic frequency, thereby restricting the development for actual operation. Accordingly, this study investigated the dynamic model of rolling bearings and explored the benefits of the coupled hybrid stochastic resonance (CHSR) method for identifying weak signal signatures. In addition, we proposed multi-objective optimization and established a dynamic model of a rolling bearing with four degrees of freedom under a rotor system with external excitation. Overall, the proposed system offers three main advantages: (1) the dynamic model facilitates correspondence with real vibration signals; (2) the CHSR method can process two-dimensional signals and overcome the saturation phenomenon, which enhances the weak useful signal signature describing machinery health; and (3) the cross-correlation spectral kurtosis and the critical amplitude are defined within the multi-objective function to adaptively optimize the parameter adjustment of the CHSR. Thereafter, the proposed method exhibited adequate enhancement ability integrated the study on dynamic simulation and machinery bearings of wind power generator. Moreover, the applied machine learning model further clarified the superior performance of CHSR method in identifying the weak fault signature.

An adaptive stochastic resonance detection method based on a fast artificial fish swarm algorithm

A new stochastic resonance method that is based on a fast artificial fish swarm algorithm has been proposed in an effort to address the adaptive parameter-induced stochastic resonance for weak signal detection’s slow convergence time. The target evaluation function for the system is the output signal-to-noise ratio. The method of scale transformation and amplitude compression is used to pre-process the high frequency and large parameter signals. To achieve fast adaptive detection that applies to weak communication signals, the stochastic resonance system’s characteristics are used to constrain the optimization iteration rules.According to the simulation results, the fast artificial fish swarm method has significantly better optimization efficiency and achieves the same optimization results as the basic artificial fish swarm algorithm while reducing convergence time by 74.89%.

Stochastic Resonance with Parameter Estimation for Enhancing Unknown Compound Fault Detection of Bearings.

Although stochastic resonance (SR) has been widely used to enhance weak fault signatures in machinery and has obtained remarkable achievements in engineering application, the parameter optimization of the existing SR-based methods requires the quantification indicators dependent on prior knowledge of the defects to be detected; for example, the widely used signal-to-noise ratio easily results in a false SR and decreases the detection performance of SR further. These indicators dependent on prior knowledge would not be suitable for real-world fault diagnosis of machinery where their structure parameters are unknown or are not able to be obtained. Therefore, it is necessary for us to design a type of SR method with parameter estimation, and such a method can estimate these parameters of SR adaptively by virtue of the signals to be processed or detected in place of the prior knowledge of the machinery. In this method, the triggered SR condition in second-order nonlinear systems and the synergic relationship among weak periodic signals, background noise and nonlinear systems can be considered to decide parameter estimation for enhancing unknown weak fault characteristics of machinery. Bearing fault experiments were performed to demonstrate the feasibility of the proposed method. The experimental results indicate that the proposed method is able to enhance weak fault characteristics and diagnose weak compound faults of bearings at an early stage without prior knowledge and any quantification indicators, and it presents the same detection performance as the SR methods based on prior knowledge. Furthermore, the proposed method is more simple and less time-consuming than other SR methods based on prior knowledge where a large number of parameters need to be optimized. Moreover, the proposed method is superior to the fast kurtogram method for early fault detection of bearings.

Optimal Noise-Boosted Estimator Design Via Adaptive Stochastic Resonance

In signal estimation, an optimal estimator is frequently unachievable because its closed form may not be analytically tractable or is too complex to implement. Alternatively, one can turn to suboptimal yet easily implementable estimators for practical signal estimation tasks. In this paper, an optimal noise-boosted estimator is designed and the adaptive stochastic resonance method is implemented to simultaneously exploit the beneficial role of the injected noise as well as the learning ability of the estimator parameter. Aiming to effectively improve the estimation performance, we use the kernel function method to find an approximate solution for the probability density function (PDF) of the optimal injected noise. During this process, the noise PDF and the estimator parameter establish a finite-dimensional non-convex optimization space for maximizing the estimation performance, which is adaptively searched by the sequential quadratic programming (SQP) algorithm at each iteration. Two representative estimation problems are explored. The obtained results demonstrate that this adaptive stochastic resonance method can improve the performance of the suboptimal estimators and bring it very close to that of the optimal estimator.

Piecewise Hybrid System with Cross-Correlation Spectral Kurtosis for Fault Diagnosis in Rolling Bearing of Wind Power Generator

As the core equipment of wind turbines, rolling bearings affect the normal operation of wind power generators, resulting in huge economic losses and significant social impacts in the case of faults. Most faults are not easily found because of the small vibration response of these rolling bearings that operate in harsh conditions. To address the problem that the fault identifications of rolling bearings are disturbed by the strong noise in wind power generators, an adaptive nonlinear method based on a piecewise hybrid stochastic resonance system with a novel cross-correlation spectral kurtosis is proposed. Then, the vibration signals collected from the fault point of the outer and inner rings are used to clarify the outstanding capability of the proposed method when compared with the maximum cross-correlation-kurtosis-based unsaturated stochastic resonance method. Furthermore, the machine learning method based on the medium tree was adopted to further prove the excellent performance of the piecewise hybrid stochastic resonance system with a novel cross-correlation spectral kurtosis for realizing the efficient detection of rolling bearing faults in wind power generators, which has important innovation significance and practical engineering value for ensuring the safe and stable operation of wind turbines.