Adaptive Stochastic Resonance Method Research Articles

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.

Dominant Frequency Extraction for Operational Underwater Sound of Offshore Wind Turbines Using Adaptive Stochastic Resonance

Underwater sound generated by the rapidly increasing offshore wind farms worldwide greatly affects the underwater soundscape and may cause long-term cumulative effects on sound-sensitive marine organisms. However, its analysis and impact assessment are heavily interfered with by underwater ambient noise. In this study, an adaptive stochastic resonance method is proposed to extract the dominant frequency of wind turbine operational sound when heavy noise is present. In particular, a time–frequency–amplitude fusion index was proposed to guide the parameter tuning of an adaptive stochastic resonance system, and an equilibrium optimizer based on the physical dynamic source–sink principle was adopted to optimize the parameter-tuning process. The results from the simulation and field data showed that the dominant frequency of operational sound was extracted adaptively. For field data with wind speeds of 4.13–6.15 m/s (at 90 m hub height), the extracted dominant frequency varied with wind speed between 90 and 107 Hz, and it was highly correlated with the wind turbine rotor speed monitored synchronously in the air, with a correlation coefficient of 0.985. Compared to other existing methods, our method has a higher output signal-to-noise ratio and a shorter running time.

SNR gain enhancement in a generalized matched filter using artificial optimal noise

For a weak signal buried in a given background noisy environment, a generalized matched filter composed of nonlinearities and weight coefficients is investigated by exploring the potential benefit of the artificial noise. With the output signal-to-noise ratio (SNR) of the conventional linear matched filter as a benchmark, the SNR gain of the generalized matched filter is proven to be possibly improved by adding an optimal noise into the easily implemented nonlinearity. From the practical point of view, even if the filter itself has an adaptability to the noisy environment, the approach of adaptive stochastic resonance still finds an optimal non-zero amount of added noise to enhance the SNR gain of the generalized matched filter. Interestingly, the optimal added noise found by the adaptive stochastic resonance method can also maximize another meaningful measure of the mean residence time (MRT), which provides more physical insight to the generalized matched filter in the sense of the noise-enhanced stability phenomenon. These obtained results indicate an extended application of the incorporation of noise in the nonlinear filter design.

Incipient fault diagnosis of planetary gearboxes based on an adaptive parameter-induced stochastic resonance method

The stochastic resonance (SR) method is commonly used in incipient fault diagnosis to extract weak fault features from complex diagnostic signals. However, the extraction effect of a SR system is highly dependent on the choice of system parameters as well as the complexity of input signals. To solve this problem, the present study proposes an adaptive parameter-induced SR method, in which high pass filter and Teager energy operator (TEO) are combined to pre-process the original signal while the grasshopper optimization algorithm is introduced to optimize the SR system parameters. The proposed method is employed to diagnose a set of experimental vibration signals of a planetary gearbox with incipient localized root crack and incipient distributed surface wear as well, leading to satisfactory diagnosis results. Comparing with the existing adaptive stochastic resonance methods, the present method claims the merits of a high signal-to-noise ratio and low computation cost.

Adaptive stochastic resonance quantified by a novel evaluation index for rotating machinery fault diagnosis

Stochastic resonance (SR) provides the enhancement of fault characteristic signals with the assistance of noise. The performance of adaptive SR must be evaluated using an appropriate index to automatically enhance various characteristic signals. This paper proposes a weighted impulse (WI) index to evaluate the performance of the adaptive general scale transformation SR (AGSTSR) in rotating machinery fault diagnosis and uses an intelligent optimization algorithm to obtain the optimal WI. The comparison results in the simulation experiment revealed that the proposed WI-based AGSTSR method presented the fault characteristics more clearly than the adaptive SR method based on the impulse index or weighted kurtosis index. Moreover, the proposed method offered the best anti-noise performance in the simulation experiment. Finally, two experimental case studies validated that the proposed method can adaptively realize early fault diagnosis of rotating machinery through the analysis of weak fault characteristics.

A Novel Adaptive Stochastic Resonance Method Based on Tristable System and its Applications

Stochastic resonance systems have the advantages of converting noise energy into signal energy, and have great potential in the field of signal detection and extraction. Aiming at the problems of the performance of classical stochastic resonance system whose model is not perfect enough and the correlation coefficients between parameters is too large to be optimized by algorithm, then a novel model of the tristable potential stochastic resonance system is proposed. The output SNR formula of the model is derived and analyzed, and the influence of its parameters on the model is clarified. Compared with the piecewise linear model by numerical simulation, the correctness of the formula and the superiority of the model are verified. Finally, the model and the classical tristable model are applied to bearing fault detection in which the genetic algorithm is used to optimize the parameters of the two systems. The results show that the model has better detection effects, which prove that the model has a strong potential in the field of signal detection.

Vibration-based fault diagnosis of the natural gas compressor using adaptive stochastic resonance realized by Generative Adversarial Networks

The compressor as an important energy transmission equipment is widely used in the natural gas pipelines to pressurize natural gas, which is prone to fail due to the characteristics of high pressure, flammability and corrosion of the natural gas. The faulty compressors may cause natural gas leakage, transmission interruption, and even explosion. Vibration monitoring and fault diagnosis of the natural gas compressor is an effective technology to ensure its security. Due to the strong noise interference, the traditional vibration diagnostic methods are difficult to obtain better effects. Stochastic resonance (SR) is a useful technology that can make full use of the noise components contained in the vibration signals to enhance the weak fault features to complete fault diagnosis. However, the applications of SR in fault diagnosis are faced with many problems, such as the difficulty of parameter selection and the need for intensive data. To solve them, an adaptive generation model of SR parameters is established by using Generative Adversarial Networks (GAN), an adaptive SR-GAN method is accordingly proposed for completing the fault diagnosis of a natural gas compressor. The simulation experiment and field data analysis are adopted to verify the effectiveness of the proposed method. The results indicate that the proposed method can improve diagnostic accuracy by 2.07% compared to the traditional adaptive SR method realized by multilayer perceptron neural network, and improve the signal-to-noise ratio by 2.25 dB at most compared with the other three methods. Moreover, the proposed method still has higher accuracy under the condition of small sample sizes. The proposed method can expand the sample when the sample size is smaller, so that the model can contain completely the operating conditions to improve the accuracy of fault diagnosis. It provides a new idea for the vibration monitoring of natural gas compressors.

Rolling Bearing Fault Diagnosis Based on Adaptive Multiparameter-Adjusting Bistable Stochastic Resonance

The weak-signal detection technologies based on stochastic resonance (SR) play important roles in the vibration-based health monitoring and fault diagnosis of rolling bearings, especially at their early-fault stage. Aiming at the parameter-fixed vibration signals in practical engineering, it is feasible to diagnose the potential rolling bearing faults through adaptively adjusting the SR system parameters, as well as other generalized parameters such as the amplitude-transformation coefficient and scale-transformation coefficient. However, extant adaptive adjustment methods focus on the system parameters, while the adjustments of other adjustable parameters have not been fully studied, thus limiting the detection performance of the adaptive SR method. In order to further enhance the detection performance of adaptive SR methods and extend their application in rolling bearing fault diagnosis, an adaptive multiparameter-adjusting SR (AMPASR) method for bistable systems based on particle swarm optimization (PSO) algorithm is proposed in this paper. This method can produce optimal SR output through adaptively adjusting multiparameters, thus realizing fault feature extraction and further fault diagnosis. Furthermore, the influence of algorithm parameters on the optimization results is discussed, and the optimization results of the Langevin system and the Duffing system are compared. Finally, we propose a weak-signal detection method based on the AMPASR of the Duffing system and employ three diagnosis examples involving inner ring fault, outer ring fault, and rolling element fault diagnoses to demonstrate its feasibility in rolling bearing fault diagnosis.

Adaptive Stochastic Resonance Method Based on Quantum Genetic Algorithm and its Application in Dynamic Characteristic Identification of Bridge GNSS Monitoring Data

Bridge dynamic monitoring based on GNSS has become an important means of monitoring bridge structure. GNSS dynamic monitoring signals are often overwhelmed by strong noises and multipath errors. Thus the conventional data processing methods such as Fourier transform, wavelet analysis, and others have poor denoising effect or obtain unconspicuous dynamic characteristics from weak vibration signals. To solve this problem, the present study proposes a new adaptive stochastic resonance method based on quantum genetic algorithm with known frequency as optimal parameter. Analyzing the simulation signals not only verifies the validity and scientificity of the method, but also analyzes its frequency extraction effect in the approximate error range of target frequency with different noise intensity. A notable bridge vibration frequency is obtained when the new method is applied to analyze the bridge dynamic monitoring data based on GNSS.

A Adaptive Stochastic Resonance Method Based on Two-Dimensional Tristable Controllable System and Its Application in Bearing Fault Diagnosis

At present, most systems with good performance have more parameters. However, increasing the number of parameters lead to increasing the difficulties of parameter optimization, thus reducing the system’s feasibility. To solve this problem, a model of controllable coupled stochastic resonance system is proposed. Firstly, the formula of the output signal-to-noise ratio of the model is derived and analyzed. Then the accuracy of the formula’s derivation and results is proved by numerical simulation. It provides a theoretical basis for adjusting the parameters and coupled coefficients of the control system to induce a stochastic resonance in the controlled system or make it much stronger. Finally, better system parameters are obtained by genetic algorithm for the controlled system (tristable system), and then better system performance is obtained by adjusting the parameters and coupled coefficient of the control system (monostable system). The model is applied into the bearing fault detection and the results show that the model achieves better performance without increasing the complexity of parameter optimization, and has great practical value in weak signal detection.

An adaptive stochastic resonance method based on multi-agent cuckoo search algorithm for bearing fault detection

Bearing is widely used in the rotating machinery and prone to failure due to the harsh working environment. The bearing fault-induced impulses are weak because of poor background noise, long vibration transmission path, and slight fault degree. Therefore, the bearing fault detection is difficult. A novel adaptive stochastic resonance method based on multi-agent cuckoo search algorithm for bearing fault detection is proposed. Stochastic resonance (SR) is like a nonlinear filter, which can enhance the weak fault-induced impulses while suppressing the noise. However, the parameters of the nonlinear system exert an influence on the SR effect, and the optimal parameters are difficult to be found. Multi-agent cuckoo search (MACS) algorithm is an excellent heuristic optimization algorithm and can be used to search the parameters of nonlinear system adaptively. Two bearing fault signals are used to validate the effectiveness of our proposed method. Three other adaptive SR methods based on cuckoo search algorithm, particle swarm optimization or genetic algorithm are also used for comparison. The results show that MACS can find the optimal parameters more quickly and more accurately, and our proposed method can enhance the fault-induced impulses efficiently.

Weak-fault diagnosis using state-transition-algorithm-based adaptive stochastic-resonance method

In the early fault period of high-speed train systems, the interested characteristic signals are relatively weak and easily submerged in heavy noise. In order to solve this problem, a state-transition-algorithm (STA)-based adaptive stochastic resonance (SR) method is proposed, which provides an alternative solution to the problem that the traditional SR has fixed parameters or optimizes only a single parameter and ignores the interaction between parameters. To be specific, the frequency-shifted and re-scaling are firstly used to pre-process an actual large signal to meet the requirement of the adiabatic approximate small parameter. And then, the signal-to-noise ratio is used as the optimization target, and the STA-based adaptive SR is used to synchronously optimize the system parameters. Finally, the optimal extraction and frequency recovery of a weak characteristic signal from a broken rotor bar fault are realized. The proposed method is compared with the existing methods by the early broken rotor bar experiments of traction motor. Experiment results show that the proposed method is better than the other methods in extracting weak signals, and the validity of this method is verified.

Sound-aided vibration weak signal enhancement for bearing fault detection by using adaptive stochastic resonance

Adaptive stochastic resonance (ASR) has been proven effective in enhancing weak periodic signals that are submerged in heavy background noise. Given such benefit, ARS has also been applied in detecting bearing faults based on vibration signal analysis. However, when the vibration has an extremely low signal-to-noise ratio (SNR), the fault characteristic frequency may not be accurately enhanced via the traditional ASR. To address this problem, this paper designs the sound-aided vibration signal ASR (SAVASR) method, which procedures are summarized as follows. First, the bearing sound and vibration signals are demodulated. Second, the envelope vibration signal is adaptively enhanced by moving a sliding window along the time axis of the envelope sound signal. Third, the optimized fused signal is sent to the ASR system, in which the parameters are adaptively adjusted based on a synthetic evaluation index. Fourth, the bearing fault is detected from the spectrum of the optimal SAVASR output signal. Qualitative and quantitative analyses are performed to evaluate and compare the performance of SAVASR with that of ASR, where only the vibration signal is processed. Given its unique approach in detecting weak signals by fusing multiple sensor information, SAVASR shows high potential in automatically detecting bearing faults especially under low SNR conditions.

An improved adaptive stochastic resonance with general scale transformation to extract high-frequency characteristics in strong noise

The idea of general scale transformation is introduced in detail. Based on this idea, an improved adaptive stochastic resonance (SR) method is proposed to extract weak signal features. Different periodic signals are considered to verify the proposed method. Compared with the normalized scale transformation, the output signal-to-noise ratio (SNR) of the proposed method is increased to a greater extent. Further, the influences of some key parameters on the responses of the two methods are discussed minutely. Results show that the improved adaptive SR method with general scale transformation is obviously superior to the traditional normalized scale transformation that is used in the former literatures. For different noise intensities and time scales, the proposed approach can always obtain the optimal response of SR to enhance the weak signal characteristics.

A novel adaptive stochastic resonance method based on coupled bistable systems and its application in rolling bearing fault diagnosis

Abstract Stochastic resonance (SR), as a typical noise-assisted signal processing method, has been extensively studied in weak signal detection by virtue of the advantage of using noise to enhance the feature of periodic signal. And how to better apply the SR method in engineering signal processing has always been the research hotspot. In this paper, a novel adaptive SR method based on coupled bistable systems (ACBSR) is proposed to further improve the performance of SR method for weak signal detection. Compared with the cascaded bistable SR system, the suggested coupled bistable SR (CBSR) system can enhance the target signal while suppressing the low-frequency and high-frequency interferences, whose output behavior exhibits good bandpass filtering characteristic. In addition, a weighted spectral peak signal-to-noise ratio (WPSNR) index is constructed by using spectral peak SNR, spectral correlation coefficient and zero-crossing ratio to serve as the measurement index of SR for periodic signal detection. The constructed WPSNR index is simple in form and easy to calculate, which can quantitatively evaluate the resonance effect of periodic signal, even though the target signal frequency cannot be estimated accurately. And the combination of WPSNR index and the CBSR system is beneficial to improve the performance of SR method in rolling bearing fault diagnosis. Experiments and engineering application are performed to verify the effectiveness and superiority of the proposed ACBSR method in comparison with the traditional SR method.

An adaptive stochastic resonance method based on grey wolf optimizer algorithm and its application to machinery fault diagnosis

Stochastic resonance (SR) is widely used as an enhanced signal detection method in machinery fault diagnosis. However, the system parameters have significant effects on the output results, which makes it difficult for SR method to achieve satisfactory analysis results. To solve this problem and improve the performance of SR method, this paper proposes an adaptive SR method based on grey wolf optimizer (GWO) algorithm for machinery fault diagnosis. Firstly, the SR system parameters are optimized by the GWO algorithm using a redefined signal-to-noise ratio (SNR) as optimization objective function. Then, the optimal SR output matching the input signal can be adaptively obtained using the optimized parameters. The proposed method is validated on a simulated signal detection and a rolling element bearing test bench, and then applied to the gear fault diagnosis of electric locomotive. Compared with the conventional fixed-parameter SR method, the adaptive SR method based on genetic algorithm (GA-SR) as well as the well-known fast kurtogram method, the proposed method can achieve a greater accuracy. The results indicated that the proposed method has great practical values in engineering.

An improved adaptive stochastic resonance method for improving the efficiency of bearing faults diagnosis

The general scale transformation (GST) method is used in the bistable system to deal with the weak high-frequency signal submerged into the strong noisy background. Then, an adaptive stochastic resonance (ASR) method with the GST is put forward and realized by the quantum particle swarm optimization (QPSO) algorithm. Through the bearing fault simulation signal, the ASR method with the GST is compared with the normalized scale transformation (NST) stochastic resonance (SR). The results show that the efficiency of the GST method is higher than the NST in recognizing bearing fault feature information. In order to simulate the actual engineering environment, both the adaptive GST and the NST methods are implemented to deal with the same experimental signal, respectively. The signal-to-noise ratio (SNR) of the output is obviously improved by the GST method. Specifically, the efficiency is improved greatly to extract the weak high-frequency bearing fault feature information. Moreover, under different noise intensities, although the SNR is decreased versus the increase of the noise intensity, the ASR method with the GST is still better than the traditional NST SR. The proposed GST method and the related results might have referenced value in the problem of weak high-frequency feature extraction in engineering fields.

An adaptive stochastic resonance method for weak fault characteristic extraction in planetary gearbox

Planetary gearbox is widely used in rotating machinery and prone to damage and failure due to heavy load and complex operating conditions. Furthermore, due to heavy background noise and complicated transmission path, the fault characteristics imbedded in the acquired signals is very weak and difficult to be extracted. Therefore, it is a challenge task for extracting fault characteristics of planetary gearboxes. To tackle this task, this paper proposes an adaptive stochastic resonance method for weak fault characteristic extraction of planetary gearbox, where a chaos ant colony algorithm characterized global optimization ability is employed to achieve adaptive matching between potential parameters and thereby overcoming the local optimization shortcoming of traditional stochastic resonance. Simulation and planetary gearbox experiments with a missing tooth and broken tooth validate the effectiveness of the proposed method, respectively. The results show that the proposed method is not only able to extract weak fault characteristics but also superior to singular value decomposition method.

Novel synthetic index-based adaptive stochastic resonance method and its application in bearing fault diagnosis

Stochastic resonance (SR), which is characterized by the fact that proper noise can be utilized to enhance weak periodic signals, has been widely applied in weak signal detection. SR is a nonlinear parameterized filter, and the output signal relies on the system parameters for the deterministic input signal. The most commonly used index for parameter tuning in the SR procedure is the signal-to-noise ratio (SNR). However, using the SNR index to evaluate the denoising effect of SR quantitatively is insufficient when the target signal frequency cannot be estimated accurately. To address this issue, six different indexes, namely, power spectral kurtosis of the SR output signal, correlation coefficient between the SR output and the original signal, peak SNR, structural similarity, root mean square error, and smoothness, are constructed in this study to measure the SR output quantitatively. These six quantitative indexes are fused into a new synthetic quantitative index (SQI) via a back propagation neural network to guide the adaptive parameter selection of the SR procedure. The index fusion procedure reduces the instability of each index and thus improves the robustness of parameter tuning. In addition, genetic algorithm is utilized to quickly select the optimal SR parameters. The efficiency of bearing fault diagnosis is thus further improved. The effectiveness and efficiency of the proposed SQI-based adaptive SR method for bearing fault diagnosis are verified through numerical and experiment analyses.

Quantitative evaluation on the performance and feature enhancement of stochastic resonance for bearing fault diagnosis

Stochastic resonance (SR) has been widely applied in the field of weak signal detection by virtue of its characteristic of utilizing noise to amplify useful signal instead of eliminating noise in nonlinear dynamical systems. How to quantitatively evaluate the performance of SR, including the enhancement effect and the degree of waveform distortion, and how to accurately extract signal amplitude have become two important issues in the research on SR. In this paper, the signal-to-noise ratio (SNR) of the main component to the residual in the SR output is constructed to quantitatively measure the enhancement effect of the SR method. And two indices are constructed to quantitatively measure the degree of waveform distortion of the SR output, including the correlation coefficient between the main component in the SR output and the original signal, and the zero-crossing ratio. These quantitative indices are combined to provide a comprehensive quantitative index for adaptive parameter selection of the SR method, and eventually the adaptive SR method can be effective in enhancing the weak component hidden in the original signal. Fast Fourier Transform and Fourier Transform (FFT+FT) spectrum correction technology can extract the signal amplitude from the original signal and effectively reduce the difficulty of extracting signal amplitude from the distorted resonance output. The application in vibration analysis for bearing fault diagnosis verifies that the proposed quantitative evaluation method for adaptive SR can effectively detect weak fault feature of the vibration signal during the incipient stage of bearing fault.