Weak signal detection method based on novel composite multistable stochastic resonance

The weak signal detection method based on stochastic resonance is usually used to extract and identify the weak characteristic signal submerged in strong noise by using the noise energy transfer mechanism.We propose a novel composite multistable stochastic-resonance(NCMSR)model combining the Gaussian potential model and an improved bistable model.Compared with the traditional multistable stochastic resonance method,all the parameters in the novel model have no symmetry,the output signal-to-noise ratio can be optimized and the output amplitude can be improved by adjusting the system parameters.The model retains the advantages of continuity and constraint of the Gaussian potential model and the advantages of the improved bistable model without output saturation,the NCMSR model has a higher utilization of noise.Taking the output signal-to-noise ratio as the index,weak periodic signal is detected based on the NCMSR model in Gaussian noise andαnoise environment respectively,and the detection effect is good.The application of NCMSR to the actual detection of bearing fault signals can realize the fault detection of bearing inner race and outer race.The outstanding advantages of this method in weak signal detection are verified,which provides a theoretical basis for industrial practical applications.

Adaptive stochastic resonance method for weak signal detection based on particle swarm optimization

In order to solve the parameter adjustment problems of adaptive stochastic resonance system in the areas of weak signal detection,this article presents a new method to enhance the detection efficiency and availability in the system of two-dimensional Duffing based on particle swarm optimization.First,the influence of different parameters on the detection performance is analyzed respectively.The correlation between parameter adjustment and stochastic resonance effect is also discussed and converted to the problem of multi-parameter optimization.Second,the experiments including typical system and sea clutter data are conducted to verify the effect of the proposed method.Results show that the proposed method is highly effective to detect weak signal from chaotic background,and enhance the output SNR greatly.

Wigner-Matrix-Based Normality Test and Application to Weak Signal Detection in SISO/SIMO Systems

Based on the asymptotic spectral distribution of Wigner matrices, a new normality test method is proposed via reforming the white noise sequence. In this work, the asymptotic cumulative distribution function （CDF） of eigenvalues of the Wigner matrix is deduced. A numerical Kullback-Leibler divergence of the empiric-d spectral CDF based on test samples from the deduced asymptotic CDF is established, which is treated as the test statistic. For validating the superiority of our proposed normality test, we apply the method to weak SIPSK signal detection in the single-input single-output （SISO） system and the single-input multiple-output （SIMO） system. By comparing with other common normality tests and the existing signal detection methods, simulation results show that the proposed method is superior and robust.

Multi-scale bistable stochastic resonance array: A novel weak signal detection method and application in machine fault diagnosis

Weak signal detection based on stochastic resonance （SR） can hardly succeed when noise intensity exceeds the optimal value of SR. This paper explores a novel parallel bistable SR array mechanism by decomposed multi-scale noises from input signal. A smoother output with lower noise is obtained from the combination of colored noise SR ellect and parallel bistable SR array. The influence of noise intensity and array size on the SR effect and output noise intensity is analyzed through numerical simu- lation. A signal detection method based on the new SR mechanism and normalized scale transform is proposed for the case of heavy background noise. Simulation is conducted to confirm the effectiveness of parameter tuning and amplitude tuning of normalized scale transform on the proposed SR model. The proposed method has three advantages： the input noise intensity of each unit is reduced by wavelet decomposition; the output noise level decreases due to array ensemble average; the SR effect of each unit is optimized by normalized scale transform for high frequency signal. Experiment on bearing inner and outer race fault diagnosis has verified the effectiveness and advantages of the proposed SR model in comparison with traditional SR method and kurlogram.

Weak wide-band signal detection method based on small-scale periodic state of Duffing oscillator

The conventional Duffing oscillator weak signal detection method, which is based on a strong reference signal, has inherent deficiencies. To address these issues, the characteristics of the Duffing oscillator＇s phase trajectory in a small- scale periodic state are analyzed by introducing the theory of stopping oscillation system. Based on this approach, a novel Duffing oscillator weak wide-band signal detection method is proposed. In this novel method, the reference signal is discarded, and the to-be-detected signal is directly used as a driving force. By calculating the cosine function of a phase space angle, a single Duffing oscillator can be used for weak wide-band signal detection instead of an array of uncoupled Duffing oscillators. Simulation results indicate that, compared with the conventional Duffing oscillator detection method, this approach performs better in frequency detection intervals, and reduces the signal-to-noise ratio detection threshold, while improving the real-time performance of the system.

Method of Weak Signals Detection Based on Chaos Suppression in the Nonresonant Parametric Drive

The evolution of chaotic state of Iarenz system on the fa- miliar parameter space cabit is analyzed. Based on the principle of chaos suppression with ntmrestmaat parametric drive, the trodel of detecting weak periodic signals in strong noise is Imilt. According to the parametric equivalent relationship obtained using averaging method and rmtmmlization method, the critical values of detection parameters are determined, which lead to a sudden change of system dynamical behavior from periodic orbit to stable equilibritma point. Sinmlation results show that weak periodic signals in strong noise can be detected acomately with the proposed system. The method can obtain aoawate rane of parameter threshold through tlxxtetical analysis, and the detection criterion is rather simple, which is more convenieat for automatic detection.

Analysis of a kind of Duffing oscillator system used to detect weak signals

The stability of the periodic solution of the Duffing oscillator system in the periodic phase state is proved by using the Yoshizaw theorem, which establishes a theoretical basis for using this kind of chaotic oscillator system to detect weak signals. The restoring force term of the system affects the weak-signal detection ability of the system directly, the quantitative relationship between the coefficients of the linear and nonlinear items of the restoring force of the Duffing oscillator system and the SNR in the detection of weak signals is obtained through a large number of simulation experiments, then a new restoring force function with better detection results is established.

Re-scaling and adaptive stochastic resonance as a tool for weak GNSS signal acquisition

Weak global navigation satellite system（GNSS） signal acquisition has been a limitation for high sensitivity GPS receivers. This paper modifies the traditional acquisition algorithms and proposes a new weak GNSS signal acquisition method using re-scaling and adaptive stochastic resonance（SR）. The adoption of classical SR is limited to low-frequency and periodic signals. Given that GNSS signal frequency is high and that the periodic feature of the GNSS signal is affected by the Doppler frequency shift, classical SR methods cannot be directly used to acquire GNSS signals. Therefore, the re-scaling technique is used in our study to expand its usage to high-frequency signals and adaptive control technique is used to gradually determine the Doppler shift effect in GNSS signal buried in strong noises. The effectiveness of our proposed method was verified by the simulations on GPS L1 signals. The simulation results indicate that the new algorithm based on SR can reach-181 d BW sensitivity with a very short data length of 1 ms.

New low noise interface circuit for detecting weak current of micro-sensors

A new low noise interface circuit for detecting weak current of micro-sensors is designed.By using the transimpedance amplifier to substitute the charge amplifier,the closed-loop circuit can avoid the phase error of the charge amplifier.Therefore,the phase compensation devices will be cancelled,because there is no phase transformation through the transimpedance amplifier.As well as,by using CCCII devices to implement the high value feedback resistor of the impedance amplifier,the noise of the I-V transformation devices is reduced,comparing with the passive resistor.The floating resistor is easy to be integrated into chips,making the integration of the interface circuit of the intelligent sensors increase.Through the simulation,the phase error of the charge amplifier is almost 9°at 2 kHz and it changes with the working frequency of the micro-sensors making the phase compensation not easy.The value of the floating resistor is 250 kΩ where the bias current is 50 μA.The noise of the active resistor is 0.037 fV2/Hz,comparing with the noise of the passive resistor,which is 4.14 fV2/Hz.

A method of multi-channel reference signals acquiring in broadband ANC

In a flank array on an unmanned underwater vehicle （UUV）, self-generated noise which has broadband and colored spectrum property in frequency and spatial domain is the main factor affecting the performance of weak signal detection, so the technique of adaptive noise cancellation （ANC） as well as physical denoising and active noise cancellation are often used in practice. Because ANC is based on correlations, improvements in performance come from better correlation between reference signals and primary signals. Taking full advantage of the characteristics of flank arrays and the characteristics of information obtained from hydrophones, a new method for reference signal acquisition for adaptive noise cancellation is proposed, in which the multi-channel reference signals are obtained by accurate delaying for a given direction of arrival （DOA） and differencing between adjacent outputs of array elements. The validity of the proposed method was verified through system modeling simulations and lake experiments which showed good performance with little additional computational burden.

Study of Signal Processing Algorithm in the Receiving End of Through-the-Earth Communications of Elastic Wave

In the research of elastic wave signal detection algorithm, a method based on adaptive wavelet analysis and segmentation threshold processing of the channel noise removal methods is suggested to overcome the effect of noise, which is prcduced by absorption loss, scattering loss, reflection loss and multi-path effect during the elastic wave in the transmission undelgroound. The method helps to realize extraction and recovery of weak signal of elastic wave from the multi-path channel, and simulation study is carded out about wavelet de-noising effects of the elastic wave and obtained satisfactory results.

Low-Noise Amplification, Detection and Spectroscopy of Ultra-Cold Systems in RF Cavities

The design and development of a cryogenic Ultra-Low-Noise Signal Amplification (ULNA) and detection system for spectroscopy of ultra-cold systems are reported here for the operation in the 0.5 - 4 GHz spectrum of frequencies (the “L” and “S” microwave bands). The design is suitable for weak RF signal detection and spectroscopy from ultra-cold systems confined in cryogenic RF cavities, as entailed in a number of physics, physical chemistry and analytical chemistry applications, such as NMR/NQR/EPR and microwave spectroscopy, Paul traps, Bose-Einstein Condensates (BEC’s) and cavity Quantum Electrodynamics (cQED). Using a generic Low-Noise Amplifier (LNA) architecture for a GaAs enhancement mode High-Electron Mobility FET device, our design has especially been devised for scientific applications where ultra-low-noise amplification systems are sought to amplify and detect weak RF signals under various conditions and environments, including cryogenic temperatures, with the least possible noise susceptibility. The amplifier offers a 16 dB gain and a 0.8 dB noise figure at 2.5 GHz, while operating at room temperature, which can improve significantly at low temperatures. Both dc and RF outputs are provided by the amplifier to integrate it in a closed-loop or continuous-wave spectroscopy system or connect it to a variety of instruments, a factor which is lacking in commercial LNA devices. Following the amplification stage, the RF signal detection is carried out with the help of a post-amplifier and detection system based upon a set of Zero-Bias Schottky Barrier Diodes (ZBD’s) and a high-precision ultra-low noise jFET operational amplifier. The scheme offers unique benefits of sensitive detection and very-low noise amplification for measuring extremely weak on-resonance signals with substantial low- noise response and excellent stability while eliminating complicated and expensive heterodyne schemes. The LNA stage is fully capable to be a part of low-temperature experiments while being operated in cryogenic conditions down to about 500 mK.

Harmonicity Spectrum

Perceiving harmonic information (especially weak harmonic information) in time series has important scientific and engineering significance. Fourier spectrum and time-frequency spectrum are commonly used tools for perceiving harmonic information, but they are often ineffective in perceiving weak harmonic signals because they are based on energy or amplitude analysis. Based on the theory of Normal time-frequency transform (NTFT) and complex correlation coefficient, a new type of spectrum, the Harmonicity Spectrum (HS), is developed to perceive harmonic information in time series. HS is based on the degree of signal harmony rather than energy or amplitude analysis, and can therefore perceive very weak harmonic information in signals sensitively. Simulation examples show that HS can detect harmonic information that cannot be detected by Fourier spectrum or time-frequency spectrum. Acoustic data analysis shows that HS has better resolution than traditional LOFAR spectrum.

Anti-interference beam pattern design based on second-order cone programming optimization

When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be optimized. The existing Dolph-Chebyshev weighting method can get the lowest side lobe level under given main lobe width, but for the other non-uniform circular array and nonlinear array, the low side lobe pattern needs to be designed specially. The second order cone programming optimization （SOCP） algorithm proposed in the paper transforms the optimization of the beam pattern into a standard convex optimization problem. Thus there is a paradigm to follow for any array formation, which not only achieves the purpose of Dolph-Chebyshev weighting, but also solves the problem of the increased side lobe when the signal is at end fire direction The simulation proves that the SOCP algorithm can detect the weak target better than the conventional beam forming.

Application of local polynomial estimation in suppressing strong chaotic noise

In this paper, we propose a new method that combines chaotic series phase space reconstruction and local polynomial estimation to solve the problem of suppressing strong chaotic noise. First, chaotic noise time series are reconstructed to obtain multivariate time series according to Takens delay embedding theorem. Then the chaotic noise is estimated accurately using local polynomial estimation method. After chaotic noise is separated from observation signal, we can get the estimation of the useful signal. This local polynomial estimation method can combine the advantages of local and global law. Finally, it makes the estimation more exactly and we can calculate the formula of mean square error theoretically. The simulation results show that the method is effective for the suppression of strong chaotic noise when the signal to interference ratio is low.

Research and application of stochastic resonance in quad-stable potential system

To solve the problem of low weak signal enhancement performance in the quad-stable system,a new quad-stable potential stochastic resonance(QSR)is proposed.Firstly,under the condition of adiabatic approximation theory,the stationary probability distribution(SPD),the mean first passage time(MFPT),the work(W),and the power spectrum amplification factor(SAF)are derived,and the impacts of system parameters on them are also extensively analyzed.Secondly,numerical simulations are performed to compare QSR with the classical Tri-stable stochastic resonance(CTSR)by using the genetic algorithm(GA)and the fourth-order Runge–Kutta algorithm.It shows that the signal-to-noise ratio(SNR)and mean signal-to-noise increase(MSNRI)of QSR are higher than CTSR,which indicates that QSR has superior noise immunity than CTSR.Finally,the two systems are applied in the detection of real bearing faults.The experimental results show that QSR is superior to CTSR,which provides a better theoretical significance and reference value for practical engineering application.

Asymmetric stochastic resonance under non-Gaussian colored noise and time-delayed feedback

Based on adiabatic approximation theory,in this paper we study the asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored noise.The analytical expressions of the mean first-passage time(MFPT)and output signal-to-noise ratio(SNR)are derived by using a path integral approach,unified colored-noise approximation(UCNA),and small delay approximation.The effects of time-delayed feedback and non-Gaussian colored noise on the output SNR are analyzed.Moreover,three types of asymmetric potential function characteristics are thoroughly discussed.And they are well-depth asymmetry(DASR),well-width asymmetry(WASR),and synchronous action of welldepth and well-width asymmetry(DWASR),respectively.The conclusion of this paper is that the time-delayed feedback can suppress SR,however,the non-Gaussian noise deviation parameter has the opposite effect.Moreover,the correlation time plays a significant role in improving SNR,and the SNR of asymmetric stochastic resonance is higher than that of symmetric stochastic resonance.Our experiments demonstrate that the appropriate parameters can make the asymmetric stochastic resonance perform better to detect weak signals than the symmetric stochastic resonance,in which no matter whether these signals have low frequency or high frequency,accompanied by strong or weak noise.

Application of the Duffing Chaotic Oscillator Model for Early Fault Diagnosis-Ⅰ. Basic Theory

In this paper, the well-known Duffing equation and the nonlinear equation describing vibration of the human eardrum are introduced from elastic nonlinear system theory. According to the fact that the human ear can distinguish weak sound with small difference, the idea that the Duffing oscillator can be used to detect a weak signal and diagnose early fault of machinery is proposed. In order to obtain a model for weak signal detection via the Duffing oscillator, the first step is to seek all forms of solutions of the Duffing equation. The second step is to study global bifurcations of the Duffing equation using qualitative analysis theory of a dynamic system. That is to say, a series of bifurcations thresholds of the Duffing equation can be analyzed by the Melnikov function and a subharmonics Melnikov function. Then the three types of bifurcations thresholds varying with damping and external exciting amplitude are discussed. The analysis concludes that the bifurcation threshold corresponding to the maximum orbit of solutions outside the homo-clinic orbit of the Duffing equation can be used to detect a weak signal. Finally, the implementing model of the Duffing oscillator for weak signal detection is given.

Characteristics of piecewise linear symmetric tri-stable stochastic resonance system and its application under different noises

Weak signal detection has become an important means of mechanical fault detections. In order to solve the problem of poor signal detection performance in classical tristable stochastic resonance system(CTSR), a novel unsaturated piecewise linear symmetric tristable stochastic resonance system(PLSTSR) is proposed. Firstly, by making the analysis and comparison of the output and input relationship between CTSR and PLSTSR, it is verified that the PLSTSR has good unsaturation characteristics. Then, on the basis of adiabatic approximation theory, the Kramers escape rate, the mean first-passage time(MFPT), and output signal-to-noise ratio(SNR) of PLSTSR are deduced, and the influences of different system parameters on them are studied. Combined with the adaptive genetic algorithm to synergistically optimize the system parameters, the PLSTSR and CTSR are used for numerically simulating the verification and detection of low-frequency, high-frequency,and multi-frequency signals. And the results show that the SNR and output amplitude of the PLSTSR are greatly improved compared with those of the CTSR, and the detection effect is better. Finally, the PLSTSR and CTSR are applied to the bearing fault detection under Gaussian white noise and Levy noise. The experimental results also show that the PLSTSR can obtain larger output amplitude and SNR, and can detect fault signals more easily, which proves that the system has better performance than other systems in bearing fault detection, and has good theoretical significance and practical value.

Underwater Optical Fiber Fluorescent System for Measuring Chlorophyll-a Concentration

Using optical fiber fluorescent technology,a new method for measuring alga concentration in water is presented. The system can realize on line measurement for alga concentration using He Ne laser as the light source. It can also effectively detect weak signals. The system with a passive sensor head has such advantages as simple structure, high sensitivity and high accuracy. It has been demonstrated that this system can be used to monitor water quality and can also be used to survey some matter.