• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

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

    2022-08-31 09:56:08GangZhang張剛YuJieZeng曾玉潔andZhongJunJiang蔣忠均
    Chinese Physics B 2022年8期
    關(guān)鍵詞:張剛

    Gang Zhang(張剛) Yu-Jie Zeng(曾玉潔) and Zhong-Jun Jiang(蔣忠均)

    1School of Communication and Information Engineering,Chongqing University of Posts and Telecommunications(CQUPT),Chongqing 400065,China

    2Cyberspace Administration of Guizhou Province,Guiyang 550000,China

    Keywords: bearing fault detection,weak signal detection,piecewise linear symmetric tri-stable system,output signal-noise-ratio,adaptive genetic algorithm

    1. Introduction

    With the rapid development of mechanical fault detection technology,weak signal detection has become an important means of extracting fault characteristic signals,[1,2]but in many practical applications, fault signals are completely submerged in strong background noise. The low signal-tonoise ratio (SNR) makes traditional fault detection methods ineffective. Therefore,the effective extraction of fault signals in strong background noise is of great significance for practical engineering applications.[3,4]Traditional signal detection methods include wavelet decomposition,[5]ensemble empirical mode decomposition,[6]singular value decomposition,[7]etc. These methods are used mainly to detect signals by removing or suppressing noise, but the signals themselves are also suppressed to a certain extent at the same time. In view of this, the stochastic resonance(SR) first proposed by Benziet al.,[8]in 1981 can convert noise energy into signal energy without damaging the signal. Therefore,the SR has become a typical noise-enhancing signal method,which has been widely used in weak signal detection so far.[9]

    In recent years, many scholars have conducted extensive researches of the classical bistable stochastic resonance system(CBSR)and achieved remarkable results,but the CBSR is only suitable for small parameters that satisfy the adiabatic approximation conditions.[10]In practical applications, the adiabatic approximation conditions cannot be satisfied because most of signals are large parameters and submerged in strong background noise. In order to achieve the better detection results and solve the practical problems in engineering applications, many scholars have conducted in-depth researches of SR systems. Lenget al.[11]proposed a second-sampling SR method, which compresses the collected signal and realizes SR through a nonlinear system. Wanget al.[12]proposed a detection method to reduce the correlation among system parameters through a special construction. The tri-stable model proposed by Zhanget al.[13]and Wanget al.[14]is applicable to the case of high noise in weak signal detection, and can better detect the early faults of rotating machinery under strong background noise conditions. Qiaoet al.[15]proposed an improved fractional-order SR model that can not only suppress the multiscale noise embedded in the signal,but also better characterize performance. An unsaturated piecewise system that solves the problem of system output saturation was proposed.[16–18]An SR system was applied to the bearing fault detection,and it was found that system parameters have great influence on system performance.[19–22]Hanet al.[23]derived the escape rate for particles by means of first passage time(MFPT).The system parameters are optimized by genetic algorithm in Refs.[24,25].

    Moreover, most of the noise detected by weak signals is ideal Gaussian white noise, which cannot represent the random noise generated by non-anthropogenic activities in nature,[26]and its waveform has significant impulsive and trailing characteristics. In order to accurately simulate noise in various fields, stochastic resonance induced by Levy noise has attracted the attention of scholars in recent years. Jiaoet al.[27]studied the stochastic resonance phenomenon of asymmetric monostable systems under different Levy stable noise environments. Guet al.[28]systematically analyzed the mean first-passage time of asymmetric bistable system under Levy noise.

    Although some research progress of weak signal detection as mentioned above has been made,further analysis shows that these systems only achieve single performance improvement by increasing the number of steady states or changing the structure of the potential function. Therefore, in order to solve the problem of output saturation and improve the output SNR of the system,a piecewise linear symmetric tri-stable random resonant system is proposed in this work. Firstly,under the premise of the adiabatic approximation theory, the SNR is deduced, and the influence of each parameter of the system on the SNR is analyzed,which is helpful in achieving the optimal detection effect. Then,in order to verify the practicality of the project,numerical simulation is introduced,and the simulation result is compared with that from the classical tristable stochastic resonance system(CTSR).In order to optimize the system parameters, an adaptive genetic algorithm is used to optimize the system parameters globally. Finally,the PLSTSR is applied to the bearing fault detection in Gaussian white noise and Levy noise,and the detection results are compared with the CTSR.

    The rest of this paper is organized as follows. In Section 2 the CTSR and the PLSTSR proposed in this paper are described, and their saturation characteristics are discussed.In Section 3,the Kramers escape rate,MFPT and SNR of the PLSTSR are deduced and the effects of parameters on them are analyzed. Also the unsaturation of PLSTSR is proven and the adaptive genetic algorithm is introduced. In Section 4,the ability of PLSTSR to detect low-frequency, high-frequency,and multi-frequency signals in Gaussian white noise environment are verified. In Section 5, the practicability of the PLSTSR detection technology is verified through two bearing experiments under Gaussian white noise. In Section 6 the bearing fault detection capability of PLSTSR under Levy noise is proved, and its engineering application value is verified.In Section 7 some conclusions are drawn from the present research.

    2. PLSTSR model

    The dynamic equation of the classic stochastic resonance system is shown below.

    Fig.1. Potential function of CTSR.

    It can be seen from Fig. 2, the system parameters exert large influences on the shape of the potential function. The changing ofm1,k1, andm2affect the change inU2,L2,U1respectively. Since the potential function of the PLSTSR is composed of 6 straight lines,the steepness of the barrier wall can be adjusted arbitrarily according to the system parameters.AsU(x)increases,xalso increases linearly,so the system does not saturate.

    Fig.2. Potential function of PLSTSR.

    A cosine signals(t)=0.2cos(2π×0.01t) is simulated under no noise, and the output signal waveform of the CTSR and the PLSTSR are shown in Fig.3 and Fig.4 respectively.

    It can be seen from Fig. 3 that when the value ofAincreases from 0.2 to 0.4,the amplitude of the output signal increases significantly, and whenA>0.4, with the increase ofA,the amplitude of the output signal does not increase significantly, and it is maintained at around 1.5, the system is saturated. Figure 4 shows that as the input signal amplitude increases, the output signal amplitude increases proportionally,thus avoiding output saturation. Comparing Fig.3 with Fig.4,under the same input signal amplitude, the output signal amplitude of Fig.4 is much larger than that of Fig.3,indicating that the PLSTSR has better signal amplification capabilities than the CTSR.

    Fig.4. Output signal of PLSTSR.

    3. SNR of PLSTSR

    The output SNR is the method that is most commonly used to evaluate the performance of stochastic resonance system. Kramers escape rate and adiabatic approximation theory are used to derive the SNR of PLSTSR.Thep1(t),p2(t),andp3(t) are the residence probabilities of Brownian particles at the three stable points at timet. Ther12(t),r21(t),r23(t),andr32(t)are Kramers escape rates between stable points,respectively.TheT12,T21,T23,andT32represent the MFPTs of particles between two stable points respectively.[23]TheR12(t),R21(t),R23(t), andR32(t) are the probabilities of the particle transition between stable points at timet, respectively. According to Refs.[29,30],Taylor series expansion is performed on them under the condition of adiabatic approximation and the first term is taken as shown in Eqs.(6)and(7).

    The MFPT can describe the difficulty of particle transition between potential wells,which can affect the occurrence of SR.Equation(6)shows thatT12andT32are only related tom2,m3,k1,andk2;T21,andT23are only related tom1andk1,;the curves of MFPT under parametersm1,m2,m3,k1,andk2are shown in Figs.5 and 6

    Fig.5. Variations of MFPT(v1 →v2)with D: (a)lnT12 changes with m2,(b)lnT12 changes with m3,(c)lnT12 changes with k1,(d)lnT12 changes with k2.

    Fig.6. Variations of MFPT(v2 →v1)with D: (a)lnT21 changes with m1,(b)lnT21 changes with k1.

    It can be seen from Figs. 5 and 6 that with the increase of noise intensity,the MFPT first gradually decreases and then tends to be stable,which indicates that the noise intensity can promote the transition of particles between potential wells,thereby generating stochastic resonance. Figure 5 show that MFPT(v1→v2)increases with the increase ofm2andk2and decreases with the increase ofm3andk1,indicating that the appropriate reduction ofm2andk2or appropriate increase ofm3andk1can promote the potential of particles from both sides.In Fig.6 that with the increase ofm1andk1,MFPT(v1→v2)increases, indicating that the appropriate reduction ofm2andk2can promote the transition of particles from the middle potential well to the potential wells on both sides.[30]

    Equations(6)and(7)can be expressed by Eq.(8)and Eq.(9)respectively.

    Substituting Eqs.(10)and(11)into Eq.(9),the linear ordinary differential method is used to solve the three-way homogeneous differential equation as given below

    From Eq.(12),using the conditional probability theorem,the conditional probability shown in Eq.(14)can be obtained below.

    According to the properties of transition probability in a symmetric system,equation(16)can be obtained as

    The output power of the signal can be obtained by the Fourier transform of autocorrelation function Eq.(18)below

    3.1. Parameter selection

    According to Eq.(20),the parameters can exert great influence on the value of SNR and determine the performance of the system. So it is necessary to study the influence of system parameters on the system. Lets(t)=0.2cos(2π×0.01t),then the relationship between SNR,noise intensity and system parameters will be shown in Figs.7–12.

    In Fig.7,the PLSTSR has the characteristics of the classical stochastic resonance system. Given other parameters are fixed,with the increase of the noise intensity,the SNR shows a trend first increasing and then decreasing,where the appearing of the peak indicates that the stochastic resonance has occurred.

    Fig.7. The change of SNR in PLSTSR with D.

    Fig.8. SNR versus D and m1.

    Fig.9. SNR versus D and m2.

    Fig.10. SNR versus D and m3.

    It can be seen from Figs. 8–10, and 12 that withDand some parameters fixed,the SNR of the PLSTSR first increases and then decreases with any of the parametersm1,m2,m3,k2increasing, and its peak value also increases as parameterDincreases. Figure 11 shows that the SNR first increases and then decreases with the increase of parameterk1,which means that there is a traditional SR phenomenon. Unlike the changes of other parameters, the SNR increases with parameterk1increasing, but the position and size of the peak do not change as shown in Fig.9.

    Fig.11. SNR versus D and k1.

    Fig.12. SNR versus D and k2.

    3.2. Adaptive genetic algorithm(GA)

    The above conclusions are all analyzed and discussed with part of the parameters fixed, but the coordinates of system parameters can also affect the performance of the system.Therefore, it is necessary to optimize these parameters. For example,many optimization algorithms such as adaptive iterative algorithm are only suitable for optimizing a small number of parameters. If there are too many parameters, then problems of insufficient precision and too high a computational complexity appear. However,the PLSTSR has 5 parameters,which is not suitable for the adaptive iterative algorithm.The adaptive genetic algorithm that simulates the biological genetic process has the advantages of multi-parameter optimization and high parameter accuracy.[24,25]Therefore,in this work the adaptive genetic algorithm is adopted to optimize the parameters. The SNR is used as the fitness function and the crossover operators such as those described Eq.(21)are used to construct the exclusive operator inX′=X+?.

    The flowchart of GA is shown in Fig.11. Subsequent parameter optimization is based on a population size of 400, a genetic generation of 200, and a crossover probability of 0.4.The mutation probability of the PLSTSR is 0.1 and the mutation probability of the CTSR is 0.4.

    Fig.13. Flowchart of adaptive genetic algorithm.

    4. Numerical simulation

    4.1. Comparative analysis

    In order to further prove the performance of PLSTSR,the fourth-order Runge–Kutta algorithm is used to simulate the periodic signals(t) = 0.2cos(2π×0.01t) in the Gaussian white noise environment, and the SNR is used as a measure.[32]Its definition is shown as follows:

    The optimal parameters of the PLSTSR are obtained by using the adaptive genetic algorithm:m1=2,m2=3,m3=3.5,k1=1,andk2=2. The optimal parameters of the CTSR area1=1,b1=2,andc1=0.1. After the 10th degree polynomial fitting,the SNR curve is obtained as shown in Fig.14.In Fig.14,with the increase ofD,the SNR for each of the two systems shows a trend first increasing and then decreasing,indicating a typical stochastic resonance phenomenon, but the peak value of the PLSTSR is larger,no matter whether the ambient noise is strong or weak,the value of SNR is larger than that of the CTSR,which proves the superiority of the PLSTSR.

    Fig.14. Comparison of SNR between PLSTSR and CTSR.

    4.2. Weak signal detection

    In order to further verify the performance of PLSTSR in signal detection,single-frequency signals(low-frequency signal and high-frequency signal)and multi-frequency signals are input into PLSTSR respectively, and the time-domain waveform and spectrum of the output signal are observed and compared with those in the case of CTSR.

    4.2.1. Single-frequency signal detection

    4.2.1.1. Low-frequency signal detection

    The low-frequency signals(t)=0.2cos(2π×0.01t)and the Gaussian white noise ofD= 0.8 are used. The optimal parameters of the CTSR are given below:a1=0.4819,b1= 1.0028, andc1= 0.4003. The optimal parameters of the PLSTSR arem1= 0.0085,m2= 0.0489,m3= 0.1605,k1=0.2539,andk2=0.3316. Figures 15 and 16 are the time domains and spectrum waveforms of the input and output signals,respectively.

    Fig.15. Time domain waveforms of input and output signals: (a)low-frequency cosine input signal,(b)low-frequency cosine input signal with noise,(c)CTSR output signal,(d)PLSTSR output signal.

    Fig. 16. Powers spectrum of input signal and output signals: (a) low-frequency cosine input signal, (b) low-frequency cosine input signal with noise, (c)CTSR output signal,(d)PLSTSR output signal.

    4.2.1.2. High-frequency signal detection

    The high-frequency signals(t)=0.2cos(2π×11.5t) and the Gaussian white noise ofD=0.8 are used. The optimal parameters of CTSR area1=1.3007,b1=0.5162, andc1=0.0418. The optimal parameters of PLSTSR arem1=0.0651,m2=0.6589,m3=0.4605,k1=0.2653,andk2=0.4816. Figures 17 and 18 are the time domains and spectrum waveforms of the input and output signals,respectively.

    Fig.17. Time domain waveforms of input and output signals. (a)High-frequency cosine input signal,(b)high-frequency cosine input signal with noise,(c)CTSR output signal,(d)PLSTSR output signal.

    Fig.18.Power spectra of input signal and output signals:(a)high-frequency cosine input signal,(b)high-frequency cosine input signal with noise,(c)CTSR output signal,(d)PLSTSR output signal.

    4.2.2. Multi-frequency signal detection

    The multi-frequency signals(t)=0.1cos(2π×0.01t)+0.2cos(2π×0.03t)+0.3cos(2π×0.05t)and the Gaussian white noise ofD=0.8 are used. The optimal parameters of CTSR area1=0.2819,b1=0.7632, andc1=0.5118. The optimal parameters of PLSTSR arem1=0.0158,m2=0.0169,m3=0.3558,k1=0.2169,andk2=0.4308. Figures 19 and 20 are the time domains and spectrum waveforms of the input and output signals,respectively.

    Fig.19. Time domain waveforms of input and output signals: (a)multi-frequency input signal,(b)multi-frequency input signal with noise,(c)CTSR output signal,(d)PLSTSR output signal.

    Fig. 20. Power spectra of input signal and output signals: (a) multi-frequency input signal, (b) multi-frequency input signal with noise, (c) CTSR output signal,(d)PLSTSR output signal.

    4.2.3. Summary

    As can be seen from Figs.15–20,the PLSTSR can detect low-frequency,high-frequency,and multi-frequency signals well,indicating wide range of applications. Compared with the CTSR,the PLSTSR has very high output signal amplitude and signalto-noise ratio as shown in Tables 1 and 2.

    Table 1. Comparison of performance between different systems in weak signal detection.

    Table 2. Comparison of SNR between different systems in weak signal detection.

    5. Bearing fault detection under Gaussian white noise

    5.1. Bearing the fault detection for 6205-2RS JEM SKF model

    To prove the great potential of the PLSTSR proposed in this paper in practical engineering applications,the CTSR and PLSTSR are used to detect the bearing fault data of Case Western Reserve University(CWRU).The bearing model is 6205-2RS JEM SKF, and the experimental workbench is shown in Fig. 21. The main parameters are shown in Table 3.[33,34]Since the adiabatic approximation theory needs to satisfy the condition of small parameters,the stochastic resonance is generated by the method of second-sampling. The sampling frequency isfs=12000 Hz, the number of sampling points isN=10000, and the secondary sampling frequency isfsr=5 Hz. In order to improve the fault detection performance of the system,an adaptive genetic algorithm is used to obtain the optimal parameters. By comparing the consistency between the characteristic frequency and the detection frequency,it can be judged whether a fault occurs. The calculation of the characteristic frequency is shown in Eq.(23).

    wherefr=29.9 Hz is the rotational frequency of the bearing. By substituting the data in Table 3 into Eq. (23), the fault frequencies of the inner and outer rings of the bearing can be calculated to befBPFI=162.2 Hz andfBPFO=107.3 Hz,respectively. Secondly, the sampling frequency is set to befs=12000 Hz, the sampling pointN=10000 and the secondary sampling frequencyfsr=5 Hz to preprocess the fault signal so as to meet the adiabatic approximation condition.

    Fig.21. 6205-2RS JEM SKF deep groove ball bearing test device.

    5.1.1. Inner ring fault detection

    Figures 22(a)and 23(a)show the time–frequency diagram of the 6205-2RS JEM SKF inner ring bearing fault signal. Figures 22(b)and 23(b)are time–frequency diagrams of the fault signal after adding Gaussian white noise. Figures 22(c)and 22(d)and figures 23(c)and 23(d)show the time–frequency diagrams of the output signals of the CTSR and PLSTSR respectively. The optimal parameters of the CTSR area1=2.4876,b1=1.1249, andc1=0.003. The optimal parameters of the PLSTSR arem1=0.4312,m2=1.4347,m3=1.0996,k1=0.0342,andk2=0.0838.

    Fig. 22. Time domain waveforms of input and output signals: (a) inner ring fault input signal, (b) inner ring fault signal with noise (D=0.2), (c) CTSR output signal,(d)PLSTSR output signal.

    Fig.23. Power spectra of input signal and output signals: (a)inner ring fault input signal,(b)inner ring fault signal with noise,(c)CTSR output signal,(d)PLSTSR output signal.

    It can be seen from Figs. 22(c) and 22(d) that the amplitude of the time domain waveform of the output signal of PLSTSR is significantly larger than that of the CTSR,and the periodicity is stronger. Figures 23(c)and 23(d)show the peak of PLSTSR and CTSR atf=162 Hz(relative error is 0.12%),which are 8.748 and 32.21 respectively, so the PLSTSR is 23.462 higher than that of CTSR. The SNRs of the two systems are?13.0787 dB and?10.8274 dB respectively,and the PLSTSR is 2.2513 dB higher than the CTSR,which proves the advantage of the PLSTSR in fault signal detection.

    5.1.2. Outer ring fault detection

    Figures 24(a) and 25(a) show the time–frequency diagram of the 6205-2RS JEM SKF outer ring bearing fault signal. Figures 24(b) and 25(b) show the time–frequency diagrams of the fault signal after adding Gaussian white noise.Figures 24(c) and 24(d) and Figs. 25(c) and 25(d) show the time–frequency diagram of the output signals of the CTSR and PLSTSR respectively. The optimal parameters of the CTSR area1=0.1507,b1=0.5291,andc1=0.3201. The optimal parameters of the PLSTSR arem1= 1.9598,m2= 1.3831,m3=5.6892,k1=3.5269,andk2=4.0129.

    It can be seen from Fig. 24 that the time domain waveform of the PLSTSR output signal has stronger periodicity and larger output amplitude. It can be seen from Figs. 25(c)and 25(d) that the spectral peaks of the output signals of the two systems are both atf= 108 Hz (relative error is 0.65%), but the spectral peak of the CTSR output signal is only 2.419,while the spectral peak of the PLSTSR output signal is 1269.The SNR of PLSTSR and CTSR are?14.2030 dB and?5.5644 dB,respectively,and the PLSTSR is 7.6389 dB higher than the CTSR.

    Fig. 24. Time domain waveforms of input and output signals: (a) outer ring fault input signal, (b) outer ring fault signal with noise (D=0.8), (c) CTSR output signal,(d)PLSTSR output signal.

    Fig.25. Power spectra of input signal and output signals: (a)outer ring fault input signal,(b)outer ring fault signal with noise(D=0.8),(c)CTSR output signal,(d)PLSTSR output signal.

    5.2. Bearing fault detection under LDK UER204 model

    Currently, the experimental data which are widely used by many scholars of SR are the CWRU bearing fault data public set. Therefore, in order to verify the applicability of the PLSTSR in different scenarios, the national public data LDK UER204-type bearing is selected for the experiment. The experimental device is shown in Fig.26. The bearing structural parameters[35]are shown in Table 4. The sampling frequency is set to befs=25600 Hz,sampling pointN=20000,and the theoretical value of outer ring fault frequency is calculated to bef=107.91 Hz. Since the signal does not meet the adiabatic approximation condition either, the secondary sampling frequency is set to befsr=5 Hz.

    Fig.26. LDK UER204 bearing test device.

    Table 4. Main data of LDK UER204 bearing.

    5.2.1. Outer ring fault detection

    Figures 27(a)and 28(a)show the time–frequency diagram of the LDK UER204 bearing fault signal. Figures 27(b) and 28(b) show the time–frequency diagrams of the fault signal after adding noise. Figure 27(c) and 27(d) and figures 28(c)and 28(d) show the time–frequency diagrams of the output signals of the CTSR and PLSTSR, respectively. The optimal parameters of the CTSR area1=0.1007,b1=2.6162,andc1=0.0418. The optimal parameters of the PLSTSR arem1=1.1512,m2=1.0547,m3=1.3156,k1=0.4354, andk2=0.5677.

    Fig. 27. Time domain waveforms of input and output signals: (a) outer ring fault input signal, (b) outer ring fault signal with noise (D=0.2), (c) CTSR output signal,(d)PLSTSR output signal.

    Fig. 28. Power spectra of input signal and output signals: (a) outer ring fault input signal, (b) CTSR output signal, (c) PLSR output signal, (d) PLSTSR output signal.

    From Figs. 28(a) and 28(b), it can be seen that the fault frequency cannot be identified by directly using Fourier transform to obtain the power spectrum of the original fault signal nor the noise-added fault signal. In Figs.28(c)and 28(d),the spectral peaks of both systems are atf=107.5 Hz(relative error is 0.38%)with peaks of 0.3402 and 5.75 respectively. The SNR of the two systems are?23.1750 dB and?20.2316 dB,respectively. The PLSTSR is improved by 2.9434 dB relative to CTSR.Obviously,the PLSTSR has a larger peak and SNR,less noise interference which makes it easier to detect the fault signal.

    6. Bearing fault detection under Levy noise

    Since Gaussian white noise is an ideal noise and cannot effectively simulate the actual noise in engineering practice,non-Gaussian Levy noise is introduced in order to be more similar to the random noise in the actual engineering environment.

    6.1. Levy noise

    The characteristic function expression of Levy noise[36]is shown as follows:

    where is the characteristic parameter,which determines the smearing characteristics and impulse characteristics of its distribution.The smearing characteristics of the noise turns stronger as increases,and the impulse characteristics becomes weaker as increases.The is a symmetry parameter, which determines the symmetry of the distribution. is the scale parameter, and represents the position parameter,which determines the center position of the distribution.

    The random variables of Levy noise are generated by the Chambers–Mallows–Stuck(CMS)method.

    where the random variablesVandWare independent of each other,V ∈(?π/2,π/2) obeys a uniform distribution,Wfollows an exponential distribution with a mean of 1, andCα,β= arctan(βtan(πα/2))/α,Dα,β,σ=σ[cos(arctan(βtan(πα/2)))]?1/α.

    6.2. Bearing fault detection under LDK UER204 model

    In order to verify the ability of PLSTSR to detect th bearing fault under Levy noise, the same LDK UER204 type of bearing as that in the previous section is selected. The sampling frequency is set to befs=25600 Hz, sampling pointN=20000, and the theoretical value of outer ring fault frequency is calculated to befout=107.91 Hz. Since the signal does not meet the adiabatic approximation condition either,the secondary sampling frequency is set to befsr=5 Hz.

    Figures 29(a) and 30(a) show the time–frequency diagrams of the LDK UER204 bearing fault signal, and figures 29(b) and 30(b) display the time–frequency diagrams of the fault signal after adding Levy noise. None of the characteristic frequencies of the fault signals can be identified. Figures 29(c) and 29(d) and figures 30(c) and 30(d) show the time–frequency diagrams of the output signals of the CTSR and PLSTSR, respectively. The optimal parameters of the CTSR area1=0.7112,b1=1.562,andc1=0.2311.The optimal parameters of the PLSTSR arem1=4.4652,m2=5.0647,m3=9.0956,k1=1.3354,andk2=1.6697.

    Fig.29. Time domain waveforms of input and output signals. (a)Outer ring fault input signal, (b)outer ring fault signal with noise(D=0.2), (c)CTSR output signal,(d)PLSTSR output signal.

    Fig.30. Power spectra of input signal and output signals: (a)outer ring fault input signal,(b)outer ring fault signal with noise,(c)CTSR output signal,(d)PLSTSR output signal.

    Comparing spectra among Figs. 30(a)–30(d), only the spectral peak of PLSTSR output signal is located atf=107.5 Hz (relative error is 0.38%), the CTSR cannot detect fault frequency well in Levy noise environment. Although the noise utilization rate of PLSTSR is not ideal, the fault frequency can still be detected. The SNR at fault frequency is?19.8919 dB,and the relative input SNR is also improved by 25.684 dB,which proves the engineering application value of PLSTSR.

    7. Conclusions and perspectives

    In this work,the PLSTSR is proposed and applied to the detecting of low-frequency, high-frequency, multi-frequency signal,and bearing fault under Gaussian white noise and Levy noise. The PLSTSR is introduced, its saturation is verified,and the Kramers escape rate and MFPT are derived. Then,using the SNR as a measure,the influence of system parameters on the SNR is analyzed.Some conclusions are drawn from the present research as follows.

    (i)PLSTSR overcomes the saturation of CTSR,improves the system output SNR,and amplifies the signal amplitude.

    (ii) The adaptive genetic algorithm optimizes the system parameters collaboratively,so that the results can achieve global optimization.

    (iii) The PLSTSR can detect low-frequency, highfrequency and multi-frequency signals well, and its SNR and output amplitude are better than those of the CTSR.

    (iv) The PLSTSR is applied to the bearing fault detection of two scenarios under the Gaussian white noise, which eliminates the chance that the proposed system is only suitable for a certain bearing. The experimental results show that the PLSTSR has better large output amplitude and SNR.It is proved that the system has good theoretical significance and practical value. The details are shown in Table 5.

    (v) The PLSTSR and CTSR are applied to detecting of bearing fault under the Levy noise, which proves that the PLSTSR can also detect fault signals in a noise environment closer to engineering scenario,while the CTSR cannot detect fault signals. The specific test results are listed in Table 5.

    Table 5. Comparison of performances among different systems in bearing fault detection.

    The system proposed in this paper is a one-dimensional system. Subsequent research will apply the potential function of PLSTSR to a two-dimensional system or an underdamped system,and judge its superiority in performance.

    Acknowledgements

    Project supported by the National Natural Science Foundation of China (Grant No. 61771085), the Research Project of Chongqing Educational Commission,China(Grant Nos. KJ1600407 and KJQN201900601), and the Natural Science Foundation of Chongqing, China (Grant No.cstc2021jcyj-msxmX0836).

    猜你喜歡
    張剛
    Visualizing and witnessing first-order coherence,Bell nonlocality and purity by using a quantum steering ellipsoid in the non-inertial frame
    Steering quantum nonlocalities of quantum dot system suffering from decoherence
    2022年高考模擬試題(三)
    層林盡染
    HeTDSE:A GPU based program to solve the full-dimensional time-dependent Schr¨odinger equation for two-electron helium subjected to strong laser fields*
    最萌“海拔差”:我要給你一個(gè)“補(bǔ)齊的幸?!?/a>
    最萌“海拔差”:我要給你一個(gè)“補(bǔ)齊的幸?!?/a>
    Implementation Scheme of Two-Photon Post-Quantum Correlations?
    數(shù)列最值問題的求解策略
    活用課本習(xí)題
    亚洲第一电影网av| 老女人水多毛片| 精品久久久噜噜| 亚洲欧美日韩东京热| 97碰自拍视频| or卡值多少钱| 欧美xxxx性猛交bbbb| 黄色欧美视频在线观看| 国产免费一级a男人的天堂| 91麻豆精品激情在线观看国产| 国产一区二区三区在线臀色熟女| 麻豆国产av国片精品| 中文字幕人妻熟人妻熟丝袜美| 老熟妇乱子伦视频在线观看| 2021天堂中文幕一二区在线观| 亚洲熟妇熟女久久| 国产美女午夜福利| 久久久久久久亚洲中文字幕| 一区二区三区激情视频| 亚洲熟妇中文字幕五十中出| 国产精品美女特级片免费视频播放器| 亚洲av中文字字幕乱码综合| 午夜福利高清视频| 国产一区二区亚洲精品在线观看| av女优亚洲男人天堂| 国产 一区 欧美 日韩| 免费av不卡在线播放| 精品国产三级普通话版| 成人无遮挡网站| 亚洲男人的天堂狠狠| 亚洲va日本ⅴa欧美va伊人久久| 又粗又爽又猛毛片免费看| 久久精品影院6| 精品欧美国产一区二区三| 国产色爽女视频免费观看| 免费av不卡在线播放| 国产高清激情床上av| 久久久久久久精品吃奶| 精品久久久久久久久久久久久| 婷婷亚洲欧美| www.色视频.com| 亚洲无线在线观看| 制服丝袜大香蕉在线| 两个人视频免费观看高清| 国产亚洲av嫩草精品影院| 很黄的视频免费| 非洲黑人性xxxx精品又粗又长| 三级毛片av免费| 人妻久久中文字幕网| 久久精品国产亚洲av天美| 校园春色视频在线观看| 亚洲人成网站高清观看| 久久久久久久久中文| 看免费成人av毛片| 精品不卡国产一区二区三区| 国产爱豆传媒在线观看| 久久久午夜欧美精品| 精品久久久久久久久亚洲 | 中国美女看黄片| 亚洲国产色片| 两人在一起打扑克的视频| 蜜桃久久精品国产亚洲av| 99热这里只有是精品50| 亚洲中文日韩欧美视频| 国产精品无大码| 国产黄色小视频在线观看| 干丝袜人妻中文字幕| 中文资源天堂在线| 一a级毛片在线观看| 亚洲欧美日韩卡通动漫| 国产综合懂色| 成人特级黄色片久久久久久久| 久久久久久伊人网av| www.www免费av| 亚洲天堂国产精品一区在线| 国产精品久久久久久久电影| 久久精品综合一区二区三区| 又爽又黄无遮挡网站| 内射极品少妇av片p| av国产免费在线观看| 欧美成人性av电影在线观看| 99久久成人亚洲精品观看| 在线观看66精品国产| 久久精品国产清高在天天线| 毛片女人毛片| 国产亚洲精品av在线| 国产精品无大码| 少妇裸体淫交视频免费看高清| 亚洲欧美激情综合另类| 国产探花极品一区二区| 午夜福利欧美成人| 国产精品久久久久久av不卡| 日韩大尺度精品在线看网址| 老熟妇仑乱视频hdxx| 琪琪午夜伦伦电影理论片6080| 三级毛片av免费| 亚洲性久久影院| 国产一区二区三区av在线 | 久久久久久久午夜电影| 久久精品国产99精品国产亚洲性色| 免费av观看视频| 中文亚洲av片在线观看爽| 日韩欧美国产一区二区入口| 亚洲国产精品sss在线观看| www.色视频.com| 国产男人的电影天堂91| 我要看日韩黄色一级片| 久久久久九九精品影院| 国产淫片久久久久久久久| 麻豆成人午夜福利视频| 国产单亲对白刺激| 亚洲人成网站高清观看| 黄色配什么色好看| 免费观看在线日韩| 国产真实伦视频高清在线观看 | 尤物成人国产欧美一区二区三区| 黄色丝袜av网址大全| 亚洲中文日韩欧美视频| 不卡一级毛片| 国产精品av视频在线免费观看| 97热精品久久久久久| 国产精品一区二区免费欧美| 十八禁网站免费在线| 亚洲人与动物交配视频| 国产午夜精品论理片| 亚洲专区中文字幕在线| 两个人视频免费观看高清| 久久精品国产鲁丝片午夜精品 | 一进一出抽搐动态| 赤兔流量卡办理| 最好的美女福利视频网| 色播亚洲综合网| 国产综合懂色| 国产精品久久久久久亚洲av鲁大| av视频在线观看入口| 久久久久精品国产欧美久久久| 国产熟女欧美一区二区| 国产精品三级大全| 极品教师在线视频| 国产高潮美女av| 国产精品自产拍在线观看55亚洲| 日韩欧美国产在线观看| 午夜福利18| 中亚洲国语对白在线视频| 黄色欧美视频在线观看| 亚洲国产精品sss在线观看| 午夜福利在线观看吧| 亚洲在线自拍视频| 美女免费视频网站| 成年人黄色毛片网站| 赤兔流量卡办理| 3wmmmm亚洲av在线观看| 在线免费十八禁| 日日摸夜夜添夜夜添av毛片 | 99热这里只有是精品50| 18禁黄网站禁片免费观看直播| 久久午夜福利片| 日韩大尺度精品在线看网址| 久久精品夜夜夜夜夜久久蜜豆| 99久久精品国产国产毛片| 看黄色毛片网站| 婷婷色综合大香蕉| 日本欧美国产在线视频| 少妇高潮的动态图| 狂野欧美激情性xxxx在线观看| 午夜福利成人在线免费观看| 老熟妇仑乱视频hdxx| 亚洲av第一区精品v没综合| 在线播放国产精品三级| 在线观看66精品国产| 久久久久久久久大av| 日本与韩国留学比较| 欧美+日韩+精品| 欧美+亚洲+日韩+国产| 国产成人福利小说| 国产亚洲精品久久久com| 国产在视频线在精品| 日韩精品中文字幕看吧| 国产午夜福利久久久久久| 少妇的逼好多水| 99热这里只有是精品在线观看| 欧美不卡视频在线免费观看| 亚洲成人精品中文字幕电影| 欧美一区二区亚洲| aaaaa片日本免费| 国产亚洲精品综合一区在线观看| 五月伊人婷婷丁香| 少妇猛男粗大的猛烈进出视频 | 亚洲专区国产一区二区| 亚洲精品一区av在线观看| 我要看日韩黄色一级片| 夜夜夜夜夜久久久久| 尾随美女入室| 村上凉子中文字幕在线| 一级毛片久久久久久久久女| 成人鲁丝片一二三区免费| 国产精品人妻久久久久久| 97碰自拍视频| 国产精品自产拍在线观看55亚洲| 国产精品伦人一区二区| 欧美精品啪啪一区二区三区| 色噜噜av男人的天堂激情| 乱人视频在线观看| 美女 人体艺术 gogo| 欧美激情国产日韩精品一区| 热99在线观看视频| 美女cb高潮喷水在线观看| 免费一级毛片在线播放高清视频| 日本与韩国留学比较| 制服丝袜大香蕉在线| 国产v大片淫在线免费观看| 免费av观看视频| 国产免费一级a男人的天堂| 色哟哟·www| 少妇猛男粗大的猛烈进出视频 | 精品久久久久久久久久免费视频| 国产精品无大码| 国产亚洲精品久久久com| 搞女人的毛片| 亚洲无线在线观看| 成年免费大片在线观看| 又黄又爽又刺激的免费视频.| 色综合婷婷激情| 亚洲av中文av极速乱 | 国内精品宾馆在线| 91麻豆av在线| 窝窝影院91人妻| 国产精品1区2区在线观看.| 无遮挡黄片免费观看| 亚洲精品粉嫩美女一区| 亚洲男人的天堂狠狠| 身体一侧抽搐| 久久中文看片网| 少妇裸体淫交视频免费看高清| 亚洲欧美日韩高清专用| 国产又黄又爽又无遮挡在线| .国产精品久久| 久久久午夜欧美精品| 美女xxoo啪啪120秒动态图| 国产精品久久久久久久久免| 免费人成在线观看视频色| netflix在线观看网站| 女同久久另类99精品国产91| 欧美bdsm另类| 久久久久久久精品吃奶| 99久国产av精品| 日韩,欧美,国产一区二区三区 | 深夜a级毛片| 亚洲精品影视一区二区三区av| 精品久久久噜噜| 国内揄拍国产精品人妻在线| 性欧美人与动物交配| 99久久久亚洲精品蜜臀av| 69av精品久久久久久| 中文字幕av在线有码专区| 高清日韩中文字幕在线| 蜜桃亚洲精品一区二区三区| av在线观看视频网站免费| 成年人黄色毛片网站| 中国美白少妇内射xxxbb| 免费电影在线观看免费观看| 色尼玛亚洲综合影院| 国产av在哪里看| 精品欧美国产一区二区三| 亚洲色图av天堂| 俄罗斯特黄特色一大片| 看片在线看免费视频| 99热网站在线观看| 欧洲精品卡2卡3卡4卡5卡区| 少妇被粗大猛烈的视频| 蜜桃亚洲精品一区二区三区| 久久欧美精品欧美久久欧美| 成人av在线播放网站| 亚洲专区国产一区二区| 夜夜爽天天搞| 欧美日韩瑟瑟在线播放| 午夜亚洲福利在线播放| 色综合婷婷激情| 欧美精品国产亚洲| 99热这里只有是精品50| 99热只有精品国产| 精品人妻一区二区三区麻豆 | 国产91精品成人一区二区三区| 如何舔出高潮| 成人国产一区最新在线观看| 一个人观看的视频www高清免费观看| 久久久久久久久久久丰满 | 国产精品无大码| 99九九线精品视频在线观看视频| 99riav亚洲国产免费| 黄色丝袜av网址大全| 午夜福利在线在线| 毛片一级片免费看久久久久 | 国产高潮美女av| 国产av不卡久久| 中文字幕精品亚洲无线码一区| 少妇的逼水好多| 亚洲真实伦在线观看| 99九九线精品视频在线观看视频| 男人狂女人下面高潮的视频| 成人高潮视频无遮挡免费网站| 日韩精品有码人妻一区| 国产精品久久久久久av不卡| 久久国产精品人妻蜜桃| 久久热精品热| 啪啪无遮挡十八禁网站| 精品久久久久久久人妻蜜臀av| 国产午夜精品久久久久久一区二区三区 | 一个人看的www免费观看视频| 观看美女的网站| 看片在线看免费视频| 亚洲18禁久久av| 中文字幕人妻熟人妻熟丝袜美| 日本 av在线| 国产精品伦人一区二区| 成人三级黄色视频| 中出人妻视频一区二区| 97人妻精品一区二区三区麻豆| av女优亚洲男人天堂| 欧美三级亚洲精品| 日本欧美国产在线视频| 我的老师免费观看完整版| 午夜免费激情av| 国产精品1区2区在线观看.| 欧美zozozo另类| 日本熟妇午夜| av在线天堂中文字幕| 中文字幕av在线有码专区| 亚洲精品粉嫩美女一区| 精品久久久久久久人妻蜜臀av| 久久精品影院6| 99热这里只有是精品50| 欧美精品国产亚洲| 国产精品电影一区二区三区| 国产国拍精品亚洲av在线观看| 国产高清三级在线| 十八禁网站免费在线| 国产在线精品亚洲第一网站| 亚洲18禁久久av| 又黄又爽又刺激的免费视频.| 久久久久久伊人网av| 国内久久婷婷六月综合欲色啪| 日韩中字成人| 欧美极品一区二区三区四区| 久久这里只有精品中国| 又爽又黄a免费视频| 99久久精品热视频| 亚洲天堂国产精品一区在线| 他把我摸到了高潮在线观看| 成熟少妇高潮喷水视频| 亚洲精品亚洲一区二区| 在现免费观看毛片| 国产爱豆传媒在线观看| 最后的刺客免费高清国语| 看黄色毛片网站| 成年女人永久免费观看视频| 成人精品一区二区免费| 国产精品自产拍在线观看55亚洲| 欧美+日韩+精品| 少妇裸体淫交视频免费看高清| 亚洲性久久影院| 偷拍熟女少妇极品色| 中文资源天堂在线| 最近中文字幕高清免费大全6 | 综合色av麻豆| 亚洲无线观看免费| 日本免费a在线| 亚洲性久久影院| 国内毛片毛片毛片毛片毛片| 日韩,欧美,国产一区二区三区 | 免费在线观看影片大全网站| 国产精品一区www在线观看 | 欧美极品一区二区三区四区| 99久久精品热视频| 国产精品一区二区免费欧美| 变态另类丝袜制服| 色综合婷婷激情| 噜噜噜噜噜久久久久久91| 看黄色毛片网站| 最近视频中文字幕2019在线8| 日韩在线高清观看一区二区三区 | 免费人成在线观看视频色| 少妇的逼好多水| 国产精品野战在线观看| 国产精品精品国产色婷婷| 91在线观看av| 天美传媒精品一区二区| 国产黄片美女视频| 午夜老司机福利剧场| 国产熟女欧美一区二区| 午夜精品久久久久久毛片777| 22中文网久久字幕| 欧美色欧美亚洲另类二区| 村上凉子中文字幕在线| 亚洲男人的天堂狠狠| 久久99热这里只有精品18| 级片在线观看| АⅤ资源中文在线天堂| netflix在线观看网站| 免费大片18禁| 国产黄片美女视频| 免费观看的影片在线观看| 人妻夜夜爽99麻豆av| 国产人妻一区二区三区在| 国产三级中文精品| 成年女人毛片免费观看观看9| 精华霜和精华液先用哪个| 亚洲久久久久久中文字幕| 他把我摸到了高潮在线观看| 中文字幕久久专区| 舔av片在线| 欧美+日韩+精品| 欧美成人性av电影在线观看| 日本成人三级电影网站| 毛片女人毛片| 男人舔奶头视频| xxxwww97欧美| 久久精品久久久久久噜噜老黄 | or卡值多少钱| 色哟哟哟哟哟哟| 18禁黄网站禁片午夜丰满| 国产av在哪里看| 久久草成人影院| 一区福利在线观看| 日韩欧美国产在线观看| 精品久久久久久久久av| 国产伦在线观看视频一区| 日本免费a在线| 免费无遮挡裸体视频| 高清毛片免费观看视频网站| 久久热精品热| 老司机午夜福利在线观看视频| 在线观看一区二区三区| 国产精品一区二区免费欧美| 亚洲无线在线观看| 亚洲国产精品合色在线| 亚洲精品久久国产高清桃花| 精品一区二区三区人妻视频| 久久精品国产亚洲网站| 色噜噜av男人的天堂激情| 中文字幕人妻熟人妻熟丝袜美| 免费高清视频大片| 中文资源天堂在线| 欧美成人a在线观看| 成年女人看的毛片在线观看| 51国产日韩欧美| 亚洲国产精品sss在线观看| 亚洲不卡免费看| 国产精品人妻久久久影院| 赤兔流量卡办理| 搡老妇女老女人老熟妇| 一级黄色大片毛片| 在线免费十八禁| 国产精品福利在线免费观看| 直男gayav资源| 亚洲av成人av| 久久久久免费精品人妻一区二区| 69av精品久久久久久| 国产精品久久久久久久电影| 中文字幕精品亚洲无线码一区| 一级a爱片免费观看的视频| 欧美激情国产日韩精品一区| 男女之事视频高清在线观看| av天堂中文字幕网| 亚洲国产色片| 国产精品福利在线免费观看| 欧美国产日韩亚洲一区| 床上黄色一级片| 91狼人影院| 最近最新免费中文字幕在线| 一进一出抽搐gif免费好疼| 亚洲成a人片在线一区二区| 黄片wwwwww| 国产精品一区二区免费欧美| 乱人视频在线观看| 在线观看66精品国产| 成人性生交大片免费视频hd| 亚洲成人中文字幕在线播放| 午夜久久久久精精品| 久久精品综合一区二区三区| 国产精品一区二区三区四区免费观看 | 禁无遮挡网站| 在线观看av片永久免费下载| 如何舔出高潮| 免费不卡的大黄色大毛片视频在线观看 | 两性午夜刺激爽爽歪歪视频在线观看| 最后的刺客免费高清国语| 国产乱人视频| 人妻久久中文字幕网| 深夜精品福利| 久久久久免费精品人妻一区二区| 成人无遮挡网站| 大型黄色视频在线免费观看| 成人亚洲精品av一区二区| 国产成年人精品一区二区| 韩国av一区二区三区四区| 日韩av在线大香蕉| 1000部很黄的大片| 特大巨黑吊av在线直播| 亚洲18禁久久av| 国产伦一二天堂av在线观看| 久久6这里有精品| 动漫黄色视频在线观看| 欧美色欧美亚洲另类二区| 97人妻精品一区二区三区麻豆| 亚洲avbb在线观看| 精品国产三级普通话版| 99久久成人亚洲精品观看| 国产欧美日韩精品一区二区| 国产av不卡久久| 99riav亚洲国产免费| 99久久久亚洲精品蜜臀av| 无人区码免费观看不卡| 人人妻人人澡欧美一区二区| 免费在线观看成人毛片| 成人国产一区最新在线观看| 国产亚洲欧美98| 午夜a级毛片| 日韩欧美国产在线观看| 欧美精品国产亚洲| 国产av麻豆久久久久久久| 五月玫瑰六月丁香| 精品一区二区三区av网在线观看| 国产精品国产三级国产av玫瑰| 国产精品一区二区免费欧美| 欧美精品国产亚洲| 欧美高清成人免费视频www| 男女边吃奶边做爰视频| 成人精品一区二区免费| 露出奶头的视频| 午夜日韩欧美国产| 天美传媒精品一区二区| 搞女人的毛片| 欧美在线一区亚洲| 又紧又爽又黄一区二区| 春色校园在线视频观看| 日本黄大片高清| 国产精品一区www在线观看 | 免费搜索国产男女视频| 亚洲专区国产一区二区| 免费观看的影片在线观看| 免费在线观看影片大全网站| 99在线视频只有这里精品首页| 99久久久亚洲精品蜜臀av| 能在线免费观看的黄片| 亚洲精品在线观看二区| 成年免费大片在线观看| 国产一区二区在线观看日韩| av专区在线播放| 99久久无色码亚洲精品果冻| 22中文网久久字幕| 日本在线视频免费播放| 最近视频中文字幕2019在线8| 久久香蕉精品热| 成年免费大片在线观看| 天堂动漫精品| 成人国产综合亚洲| 无人区码免费观看不卡| 国产精品一及| 老司机深夜福利视频在线观看| 亚洲欧美日韩高清专用| 国产不卡一卡二| 午夜视频国产福利| 日韩欧美精品免费久久| 亚洲欧美日韩无卡精品| 亚洲三级黄色毛片| 男女视频在线观看网站免费| 成人国产一区最新在线观看| 亚洲天堂国产精品一区在线| 国产黄色小视频在线观看| 国产高潮美女av| 日本三级黄在线观看| 国产精品爽爽va在线观看网站| 国产精品久久久久久久电影| 国产精品久久久久久久久免| 国产一区二区激情短视频| av福利片在线观看| 啦啦啦啦在线视频资源| 长腿黑丝高跟| 国产精品98久久久久久宅男小说| 一级黄片播放器| 国产私拍福利视频在线观看| 成人永久免费在线观看视频| 欧美色视频一区免费| 日本 av在线| 韩国av一区二区三区四区| 国内精品宾馆在线| 国内揄拍国产精品人妻在线| 国产精品不卡视频一区二区| 午夜福利视频1000在线观看| 精华霜和精华液先用哪个| 亚洲av中文字字幕乱码综合| 18禁裸乳无遮挡免费网站照片| 美女大奶头视频| 国产伦精品一区二区三区四那| videossex国产| 久久国产乱子免费精品| 麻豆一二三区av精品| 日韩欧美精品免费久久| 亚洲成人中文字幕在线播放| 小蜜桃在线观看免费完整版高清| 美女cb高潮喷水在线观看| 久久精品国产自在天天线| 免费av观看视频| 日韩亚洲欧美综合| 亚洲美女视频黄频| 久久久久免费精品人妻一区二区| 久久久国产成人免费| 99热网站在线观看| 亚洲最大成人中文| 美女 人体艺术 gogo| 亚洲18禁久久av| 免费av不卡在线播放| 久久草成人影院| a级毛片a级免费在线|