Research On The Method Of Optical Fiber Detecting Vibration Signal Based On The PSER

Power Spectrum sub-band Energy Ratio(PSER)is the ratio of the power spectrum energy in a specific frequency band to the total power spectrum energy.In this paper,the detection method based on PSER is taken as the main method of detecting underground vibration signals by optical fiber because it can still remain stable under the noise power uncertainty.Distributed fiber Acoustic Sensing(DAS)is a fiber optic vibration sensing system based on the principle of coherent Rayleigh scattering and optical time-domain scattering,which can continuously monitor the vibration state around underground infrastructure in a large range.Its monitoring data contains rich information of underground environment and events,which has been paid more and more attention by the government,society and experts.There are two detection scenarios when using DAS to detect underground vibration signals:detecting signals with known spectrum distribution or completely unknown.For the two scenes,this paper will establish two detection methods for the local spectrum and the full spectrum.In addition,the underground vibration signal collected by DAS has the characteristics of noise power uncertainty and large amount of data,as well as the requirements of detection performance,convenient operation and detection speed.Therefore,the two methods should also have the characteristics of adapting to noise uncertainty,preferable detection performance,not requiring prior information and fast detection speed.Through theoretical analysis and experimental comparison of various detection methods,this study found that the detection performance of PSER has less fluctuation compared with other methods under noise uncertainty.Therefore,this study aims to establish the new signal detection methods based on the PSER for vibration signal detected by optical fiber.Around the construction of the PSER detection method,the main research work in this paper consists of six sections:1.The research on the characteristics of the vibration signal detected by optical fiberThe following characteristics are acquired via statistical analysis of the signal detected by optical fiber:(1)The features of optical fiber noise signals are uncertain and non-strict Gaussian white noise;(2)the characteristic frequency band of vibration signals is 50-100Hz.Data preprocessing and validation trials can be based on these characteristics.2.The research on the probability distribution for PSERThe PSER probability distribution is the theoretical foundation of the PSER-based detection methods.The PSER distribution follows the beta distribution in the absence of a signal.When there are signals,however,the PSER distribution is just approximate,and no accurate conclusion can be drawn.As a result,this paper derives the exact probability distribution of PSER in the presence of a signal,confirms that it follows the doubly non-central beta distribution,and gives the infinite double series expressions of its probability density function(Equation 3-48)and cumulative distribution function(Equation 3-47).The simulation results suggest that the PSER probability distribution derived in this study is more accurate than the approximate probability distribution in terms of the actual statistical situation.3.The research on the numerical calculation for the cumulative distribution function of PSER under signal presence.The cumulative distribution function of PSER is the basis for calculating the theoretical detection probability.According to the Mmatrix composed by the double series term in Equation 3-34,two numerical calculation methods,named divisions Ⅰ and Ⅱ,are proposed.According to the properties of the regular beta function,the error upper limit expressions of the two methods are derived respectively(Equations 4-16 and 4-26),and the corresponding numerical calculation algorithms are determined.Experiments show that there is little difference in calculation accuracy between the two methods,but the calculation time of the division I is only half of that of the division Ⅱ.Therefore,this paper uses the division I to calculate the cumulative distribution function of PSER.4.The research on the PSER detector for local power spectrum.To detect the signals with known spectral distribution,a PSER detector for local power spectrum is proposed,which takes the PSER of local spectrum as the detection statistic.In this section,the theoretical false detection probability and detection probability of the local spectral PSER detector are derived under the constant false alarm strategy.The false detection probability is only related to the number of power spectrum lines and sub-band lines but has nothing to do with the noise variance.The influences of power spectrum line number,sub-band line number,frequency band energy ratio coefficient,and local signal-to-noise ratio on detection performance are analyzed.Under the robustness criterion,the detection performance under noise uncertainty is derived.The simulation results show that the theoretical detection probability of PSER is consistent with the actual statistic.5.The research on the PSER entropy detector for full power spectrumIn order to detect completely unknown signals,a PSER entropy detector for full power spectrum is proposed,which takes full-spectrum PSER entropy as detection statistic.To calculate the mean and the variance of sample entropy,a new discrete entropy calculation framework based on interval partition and multinomial distribution is constructed.In this framework,the value range of PSER,[0,1],is divided into multiple equal interval intervals.The concepts of interval probability,interval entropy,sample entropy,interval joint entropy,sample entropy mean(PSER entropy for short),and sample entropy variance are defined.On the one hand,the formulas for calculating the variance of PSER entropy(Deduction 6.1)and sample entropy(Deduction 6.3)under signal absence are derived by using multinomial distribution.It is found that their values are only related to the number of power spectrum lines and the number of divided intervals,but not to the noise variance.On the other hand,the formulas for calculating the variance of PSER entropy(Deduction 6.4)and sample entropy(Deduction 6.6)under signal presence are derived using mixed multinomial distribution.Their values are not only related to the number of power spectrum lines and the number of divided intervals,but also related to the SNR of each power spectrum line.Under the constant false alarm strategy,this paper estabilish the PSER entropy detector for full power spectrum.This paper uses the PSER entropy and sample entropy variance calculated under the new discrete entropy calculation framework to deduce the false detection probability and detection probability of the PSER entropy of noise lower or higher than that of signal respectively.When the two cases are fused,a comprehensive decision detector is proposed,and the correction method of its false alarm probability is presented too.In the simulation experiment,the theoretical detection probability and false alarm probability of the PSER entropy detector for full power spectrum are consistent with the actual statistical results,which indicate that the deductions in this section are correct.6.Underground vibration signal detection experimentIn the case of considering and not considering the noise uncertainty,local spectrum PSER,full-spectrum PSER entropy,energy,local spectrum energy and covariance matrix detection are used to detect distributed optical fiber vibration signals respectively,and the detection performances are compared.According to the above research content,the innovation points of this paper summarize as follows:(1)Establish a numerical calculation method of the cumulative distribution function for PSER,which based on the partition of the matrix formed by the infinite double series term in the expression of the cumulative distribution function for PSER.This method is a necessary tool for caculating the detection probability of the detector based on PSER.This method can automatically determine the range of series terms involved in numerical calculation according to the preset error upper limit,and ensure the calculation accuracy.(2)Propose a PSER detector for local power spectrum to detect the vibration signal on optical fiber.Aiming at the problem of detecting specific frequency band events under noise uncertainty,this detector has the advantages of adapting to noise uncertainty,no need to estimate noise variance,and fast detection speed.(3)Propose a PSER entropy detector for full power spectrum based on the new discrete entropy calculation framework.To solve the problem of detecting signal without prior knowledge,this detector has the advantages of adapting to noise uncertainty,no need to estimate noise variance,and preferable detection performance.The comprehensive decision detector is a blind signal detector without any prior information about a signal.Theoretical analysis and experiments confirm that the local spectrum PSER and full-spectrum PSER entropy detectors are suitable for the vibration signal detected by optical fiber.They can apply to the safety monitoring of pipe networks,tunnels,and dams based on fiber optic sensing technology.