WO2021248906A1 - 光纤相位解调中偏振诱导衰落导致相位跳变修正方法 - Google Patents

光纤相位解调中偏振诱导衰落导致相位跳变修正方法 Download PDF

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WO2021248906A1
WO2021248906A1 PCT/CN2021/070278 CN2021070278W WO2021248906A1 WO 2021248906 A1 WO2021248906 A1 WO 2021248906A1 CN 2021070278 W CN2021070278 W CN 2021070278W WO 2021248906 A1 WO2021248906 A1 WO 2021248906A1
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phase
demodulation
polarization
moving average
time
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French (fr)
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李政颖
樊民朗
王洪海
吴军
王加琪
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武汉理工大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H9/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by using radiation-sensitive means, e.g. optical means
    • G01H9/004—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by using radiation-sensitive means, e.g. optical means using fibre optic sensors
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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  • the invention belongs to the technical field of optical fiber sensing, and specifically relates to a method for correcting phase jumps caused by polarization-induced fading in optical fiber phase demodulation.
  • Vibration is one of the most common phenomena in nature. Through the detection of vibration, structural health monitoring, disaster and abnormal event warnings can be realized. Vibration detection is an important research direction and application field in distributed optical fiber sensing technology.
  • the optical fiber vibration monitoring system restores the vibration information in the environment by demodulating and transmitting the phase change of the optical pulse in the optical fiber.
  • the arctangent demodulation method based on 3 ⁇ 3 fiber coupler is one of the main methods of fiber vibration demodulation. This method uses the characteristics of a 120° phase difference between the three-terminal output optical signals of a 3 ⁇ 3 fiber coupler to establish the sine and cosine variables in the arctangent operation, and uses the arctangent operation to demodulate the phase information in the optical signal.
  • the value range of the arctangent operation is (- ⁇ /2, ⁇ /2), which is extended to (- ⁇ , ⁇ ) according to the signs of the sine and cosine variables involved in the operation, so the phase value of the representative vibration demodulated by the arctangent operation Compressed at (- ⁇ , ⁇ ), a phase deconvolution algorithm is required, that is, when the difference between two adjacent demodulation phase values is greater than ⁇ , the phase value at the later time is increased or decreased by 2 ⁇ compensation value, Restore the phase change caused by the real vibration signal.
  • Practical engineering requirements. Distributed optical fiber vibration sensing technology covers a long distance.
  • the detection light pulses transmitted in the optical fiber are more likely to undergo random polarization changes due to fiber bending, force, etc., which causes the visibility of the interferometer output interference signal to change.
  • the polarization states are orthogonal, the visibility of the interference signal output by the interferometer is zero, that is, polarization cancellation occurs, resulting in a polarization-induced signal fading effect.
  • the visibility of the interference signal is small, the sine and cosine components established according to the phase difference characteristics of the output optical signal at the three ends of the 3 ⁇ 3 fiber coupler approach 0 at the same time, and are affected by electrical noise and optical noise at the same time, and the arctangent operation is distorted.
  • the phase signal restored by the phase deconvolution algorithm has wrong phase compensation, resulting in a step jump in the final demodulated vibration information, which seriously affects the application of the optical fiber vibration monitoring system in actual engineering.
  • the purpose of the present invention is to solve the above technical problems and provide a method for correcting the phase jump caused by polarization-induced fading in optical fiber phase demodulation.
  • the value and the actual demodulation phase value are compared and analyzed to determine whether there is a jump point, and then the jump point is corrected. Ensure the correctness of subsequent processing based on vibration signals.
  • a method for correcting phase jumps caused by polarization-induced fading in optical fiber phase demodulation designed by the present invention is characterized in that it includes the following steps:
  • Step 1 Select the demodulated phase when the polarization is not canceled as the historical sample data by analyzing the three-terminal output optical signal of the 3 ⁇ 3 fiber coupler in the Mach-Zinde interferometer;
  • Step 2 Use the historical sample sequence selected in step 1, to construct the demodulated phase autoregressive moving average model using time series analysis, and use the Akaike information criterion or Bayes information criterion to determine the order of the demodulated phase autoregressive moving average model, and Determine the autoregressive coefficients and moving average coefficients of the demodulated phase autoregressive moving average model by using the least squares estimation method;
  • Step 3 Express the Kalman state vector with the demodulation phase (the phase of the light transmitted in the optical fiber), and use the demodulation phase autoregressive moving average model obtained in step 2 to initialize the Kalman state transition matrix, system noise vector, and prediction output Matrix and other parameters, establish the Kalman demodulation phase prediction model, and derive the Kalman demodulation phase prediction model recursive equations;
  • Step 4 Use the created Kalman demodulation phase prediction model to predict the demodulation phase in real time, and perform the difference calculation with the actual phase demodulated by the arctangent algorithm and the phase deconvolution algorithm to determine whether the actual demodulation phase exists Jump point, if there is a jump point, the polarization state of the light needs to be judged. When the polarization state of the light is polarization destructive, the jump point needs to be corrected. The correction method is to replace the actual demodulated phase with the predicted phase value.
  • the present invention initializes the state equation and observation equation of the Kalman demodulation phase with the created demodulation phase ARMA model (demodulation phase autoregressive moving average model), effectively avoiding the difficulty in determining the parameters of the Kalman demodulation phase prediction model Problem: Using historical data to construct the demodulation phase ARMA model initialization Kalman demodulation phase prediction model has higher prediction accuracy and stability than the traditional Kalman prediction. The Kalman demodulation phase prediction model is used to predict the subsequent phase in real time. The predicted value and the actual demodulation phase are compared and analyzed to determine whether the actual demodulation phase has a step jump, and then the jump point is corrected to eliminate the demodulation There is a jump point problem in the phase;
  • Figure 1 is a flow chart of the present invention
  • Figure 2 is a structural diagram of the Mach-Zinde interferometer in the present invention.
  • the Mach-Zinde interferometer in Figure 2 consists of a 1 ⁇ 2 fiber coupler, a 3 ⁇ 3 fiber coupler, a delay fiber, and photodiodes PD1, PD2, and PD3.
  • a method for correcting phase jumps caused by polarization-induced fading in optical fiber phase demodulation is characterized in that it includes the following steps:
  • Step 1 Select the demodulated phase when the polarization is not canceled as the historical sample data by analyzing the three-terminal output optical signal of the 3 ⁇ 3 fiber coupler in the Mach-Zinde interferometer;
  • Step 2 Use the historical sample sequence selected in step 1, to construct the demodulated phase autoregressive moving average model using time series analysis, and use the Akaike information criterion or Bayes information criterion to determine the order of the demodulated phase autoregressive moving average model, and Determine the autoregressive coefficients and moving average coefficients of the demodulated phase autoregressive moving average model by using the least squares estimation method;
  • Step 3 Express the Kalman state vector by demodulation phase, and use the demodulation phase autoregressive moving average model obtained in step 2 to initialize the Kalman state transition matrix, system noise vector, predictive output matrix and other parameters to establish Kalman demodulation
  • the phase prediction model is used to derive the Kalman demodulation phase prediction model recursive equation set.
  • the present invention applies the Kalman prediction effect to the optical fiber vibration sensor, and uses the demodulated phase value to determine the Kalman state vector and parameters, and establish the solution Phase-adjusted Kalman prediction model;
  • Step 4 Use the created Kalman demodulation phase prediction model to predict the demodulation phase in real time, and perform the difference calculation with the actual phase demodulated by the arctangent algorithm and the phase deconvolution algorithm to determine whether the actual demodulation phase exists Jump point, if there is a jump point, the polarization state of the light needs to be judged. When the polarization state of the light is polarization destructive, the jump point needs to be corrected. The correction method is to replace the actual demodulated phase with the predicted phase value.
  • step 1 of the above technical solution under the condition that the polarization is not destructive, the three-terminal output optical signal of the 3 ⁇ 3 fiber coupler has a phase difference of 120°, and the three-terminal output light of the 3 ⁇ 3 fiber coupler detected by the photodetector The signals will not tend to be equal.
  • the demodulation phase at the time of non-polarization cancellation is selected as the historical sample data.
  • Step 2 of the above technical solution Utilize historical sample data Construct a demodulation phase autoregressive moving average model, the demodulation phase of the demodulation phase autoregressive moving average model at the current moment and the demodulation phase at the historical moment satisfy the following relationship:
  • ⁇ (k) is the state vector at time k
  • ⁇ (k+1) is the state vector at time k+1
  • Z(k+1) is the measurement vector at time k+1
  • w(k) is the state vector at time k
  • the system noise vector v(k+1) is the measurement noise vector at k+1
  • A(k+1,k) is the state transition matrix from k to k+1
  • H(k+1) is The predicted output matrix at k+1 time;
  • ⁇ (k) represents the Kalman state vector constructed by the demodulation phase
  • T represents the transpose of the matrix
  • ⁇ (k+1), ⁇ (k) are the phase state vectors at k+1, k, respectively, e(k+1), e(k), e(k-1),...,e(k- q+1) is the residual white noise sequence of the demodulated phase autoregressive moving average sequence, ⁇ 1 , ⁇ 2 ..., ⁇ q is the moving average coefficient;
  • K(k+1) is the Kalman gain matrix at time k+1
  • k) represents the estimation of the state vector at time k
  • Z (k+1) represents the observation vector in formula (5)
  • k) represents the single-step prediction error covariance matrix from time k to time k+1
  • H T (k+1) is represented as The prediction output matrix at k+1
  • k) is the prediction error covariance matrix at k
  • a T (k+1,k) is the state transition matrix from k to k+1
  • T is the transition Set
  • k) represents the single-step prediction error covariance matrix from time k to time k+1
  • k+1) is the error covariance matrix predicted at time k+1
  • Q(k) is the covariance matrix of w(k).
  • the covariance matrix can be obtained by calculating the residual white noise sequence in equation (1), and I is the
  • the phase deconvolution algorithm is integral, that is, the error compensation value superimposed by the convolution phase unwrapping will always exist in the subsequent phase deconvolution results.
  • the error compensation phase is corrected, in order to eliminate the error compensation of the phase deconvolution algorithm
  • the observation vector Z(k+1) needs to be corrected, that is, a cumulative amount C(k+1) is added.
  • the established Kalman demodulation phase prediction model is used to predict the demodulation phase at time k+1 based on historical statistical information and the demodulation phase at time k, namely The predicted value and the actual demodulated value are calculated to determine whether there is a jump point in the actual demodulated phase. If there is a jump point, the polarization state of the light needs to be judged. When the polarization state of the light is in polarization cancellation, it needs to be jumped. The change point is corrected, and the correction method is to replace the actual demodulated phase with the predicted phase value.
  • step 1 select the demodulated phase at the time of non-polarization cancellation as the historical sample data
  • a n is the DC component
  • B n is the AC component
  • the AC component B n of the three-terminal output light intensity of the 3 ⁇ 3 coupler approaches 0, resulting in the three-terminal output of the 3 ⁇ 3 coupler
  • the light intensity I 1 ⁇ I 2 ⁇ I 3 so the polarization state of the two interfering lights can be judged by the three-terminal output light intensity of the 3 ⁇ 3 coupler, so as to select the demodulation phase when the non-polarization cancellation is used as the historical sample data
  • the specific method for determining the order of the demodulation phase autoregressive moving average model using Akaike information criterion or Bayesian information criterion is:
  • the Akaike information criterion sets the order of the demodulated phase autoregressive moving average model to ARMA(p,q), where p,q satisfy the following relationship;
  • the Bayesian information criterion sets the order of the demodulated phase autoregressive moving average model to ARMA(p,q), where p,q satisfy the following relationship;
  • min AIC is the most suitable demodulation phase autoregressive moving average model order corresponding to the Akaike information criterion
  • min BIC is the most suitable demodulation phase autoregressive moving average model order corresponding to the Bayesian information criterion, where n is Select demodulation phase as sample quantity, Is an estimate of the variance of the model's white noise.
  • step 2 above use the selected historical demodulation phase sample sequence to establish the sample sequence required to select the ARMA model It is a stationary series, so you first need to use the graph test method to Carry out stationarity test, if the sequence meets the stationarity condition, use the sample sequence directly Build an ARMA model. If the stationarity condition is not satisfied, then the sample sequence Carry out the difference operation until the stationarity condition is satisfied, and then establish the ARMA model of the stationary sequence after the difference.
  • the created Kalman demodulation phase prediction model is used to predict the demodulated phase data in real time, and the difference is calculated with the actual phase demodulated by the arctangent algorithm and the phase deconvolution algorithm. If If the absolute value of the difference is greater than the threshold, there is a jump point.
  • the selection of the threshold depends on the noise level of the demodulation system, and is set to the variance of the demodulation phase without the vibration signal for a period of time in the past.
  • the polarization cancellation state is judged by the light intensity signal output from the three ends of the 3 ⁇ 3 fiber coupler collected by the ADC (data acquisition card). Specifically, the three-way light intensity signal is paired by the difference operation to obtain three sets of differences. The three sets of differences are all less than the set threshold, that is, it is judged as a polarization cancellation state.
  • the method for judging the polarization cancellation state in the above step 4 is to analyze the output light intensity signals I 1 , I 2 , I 3 of the 3 ⁇ 3 coupler obtained by the system.
  • N represents the estimation of the noise level of the output light intensity data of the 3 ⁇ 3 coupler collected by the ADC.
  • the actual demodulation phase ⁇ _R(k+1) is corrected, and the actual demodulation phase is replaced by the predicted phase.
  • the invention solves the problem of random step jumps in the demodulation phase due to polarization-induced fading in the optical fiber vibration demodulation system, and ensures the correctness of subsequent analysis based on vibration data.

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Abstract

本发明公开了一种光纤相位解调中偏振诱导衰落导致相位跳变修正方法，它包括如下步骤：1、选取非偏振相消时的解调相位作为历史样本数据；2、确定解调相位自回归滑动平均模型的自回归系数和滑动平均系数；3：建立卡尔曼解调相位预测模型，推导卡尔曼解调相位预测模型递推方程组；4、判断实际解调相位是否存在跳变点，如果存在跳变点需要对光的偏振态进行判断，当光的偏振态处于偏振正交时需要对跳变点进行修正，修正方式为以相位预测值代替实际解调相位。本发明保证后续基于振动信号处理的正确性。

Description

光纤相位解调中偏振诱导衰落导致相位跳变修正方法 技术领域
本发明属于光纤传感技术领域，具体涉及一种光纤相位解调中偏振诱导衰落导致相位跳变修正方法。
技术背景
振动是自然界最普遍的现象之一，通过振动的检测可以实现结构健康监测、灾害和异常事件的预警等。振动检测是分布式光纤传感技术中的一个重要研究方向和应用领域。
光纤振动监测系统通过解调传输在光纤中光脉冲的相位变化还原环境中的振动信息。基于3×3光纤耦合器的反正切解调方法是光纤振动解调主要方法之一。该方法利用3×3光纤耦合器三端输出光信号两两相位差120°的特性建立反正切运算中的正弦变量和余弦变量，采用反正切运算解调出光信号中的相位信息。反正切运算的值域为(-π/2,π/2),根据参与运算的正弦变量和余弦变量的符号扩展到(-π,π)，因此反正切运算解调的代表振动的相位值被压缩在(-π,π)，需要通过相位解卷积算法，即当两相邻解调相位值之间的差值大于π，对后一时刻相位值增加或减小2π的补偿值，还原真实的振动信号引起的相位变化。实际工程需求分布式光纤振动传感技术覆盖距离远，光纤中传输探测光脉冲更容易因为光纤弯曲、受力等发生偏振态随机变化，导致干涉仪输出干涉信号的可见度改变，当两干涉光的偏振态正交时，干涉仪输出干涉信号的可见度为零，即发生偏振相消，产生偏振诱导信号衰落效应。当干涉信号可见度较小时，根据3×3光纤耦合器三端输出光信号相位差特性建立的正弦分量和余弦分量同时趋近于0，同时受到电噪声和光噪声的影响，反正切运算存在失真，使得相位解卷积算法还原后的相位信号存在错误的相位补偿，导致最终解调振动信息存在阶跃跳变，严重影响了光纤振动监测系统在实际工程中的应用。
发明内容
本发明的目的是针对上述技术问题，提供一种光纤相位解调中偏振诱导衰落导致相位跳变修正方法，本发明利用历史不存在跳变的解调相位建立解调相位预测模型，将预测相位值和实际解调相位值进行对比分析，判断是否存在跳变点，进而对跳变点进行修正。保证后续基于振动信号处理的正确性。
为实现此目的，本发明所设计的一种光纤相位解调中偏振诱导衰落导致相位跳变修正方法，其特征在于，它包括如下步骤：
步骤1：通过对马赫增德干涉仪中3×3光纤耦合器三端输出光信号分析选取偏振不相消时的解调相位作为历史样本数据；
步骤2：利用步骤1选择的历史样本序列，采用时间序列分析方法构建解调相位自回归滑动平均模型，利用赤池信息准则或贝叶斯信息准则确定解调相位自回归滑动平均模型阶数，并利用最小二乘估计法确定解调相位自回归滑动平均模型的自回归系数和滑动平均系数；
步骤3：以解调相位(传输在光纤中光的相位)表示卡尔曼状态向量，并利用步骤2中获得的解调相位自回归滑动平均模型初始化卡尔曼状态转移矩阵、系统噪声向量、预测输出矩阵等参数，建立卡尔曼解调相位预测模型，推导卡尔曼解调相位预测模型递推方程组；
步骤4：用创建的卡尔曼解调相位预测模型，对解调相位进行实时预测，并与利用反正切算法和相位解卷积算法解调的实际相位做差运算，判断实际解调相位是否存在跳变点，如果存在跳变点需要对光的偏振态进行判断，当光的偏振态处于偏振相消时需要对跳变点进行修正，修正方式为以预测相位值代替实际解调相位。
本发明将创建的解调相位ARMA模型(解调相位自回归滑动平均模型)初始化Kalman(卡尔曼)解调相位的状态方程和观测方程，有效地避免了Kalman解调相位预测模型参数确定困难的问题；利用 历史数据构建解调相位ARMA模型初始化的Kalman解调相位预测模型相对于传统的Kalman预测具有更高的预测准确性和稳定性。通过Kalman解调相位预测模型对后续的相位进行实时预测，将预测值与实际解调相位进行对比分析，判断实际解调相位是否发生阶跃跳变，进而对跳变点进行修正，消除解调相位存在跳变点问题；
附图说明
图1为本发明的流程框图；
图2为本发明中马赫增德干涉仪结构图；
图2中的马赫增德干涉仪由1×2光纤耦合器、3×3光纤耦合器、延时光纤、光电二极管PD1、PD2和PD3。
具体实施方式
以下结合附图和实例对本发明作进一步的详细说明：
如图1和2所示的一种光纤相位解调中偏振诱导衰落导致相位跳变修正方法，其特征在于，它包括如下步骤：
步骤1：通过对马赫增德干涉仪中3×3光纤耦合器三端输出光信号分析选取偏振不相消时的解调相位作为历史样本数据；
步骤2：利用步骤1选择的历史样本序列，采用时间序列分析方法构建解调相位自回归滑动平均模型，利用赤池信息准则或贝叶斯信息准则确定解调相位自回归滑动平均模型阶数，并利用最小二乘估计法确定解调相位自回归滑动平均模型的自回归系数和滑动平均系数；
步骤3：以解调相位表示卡尔曼状态向量，并利用步骤2中获得的解调相位自回归滑动平均模型初始化卡尔曼状态转移矩阵、系统噪声向量、预测输出矩阵等参数，建立卡尔曼解调相位预测模型，推导卡尔曼解调相位预测模型递推方程组，本发明将卡尔曼预测效果运用到的光纤振动传感中，以解调相位值去确定卡尔曼的状态向量和参数，建立解调相位卡尔曼预测模型；
步骤4：用创建的卡尔曼解调相位预测模型，对解调相位进行实时预测，并与利用反正切算法和相位解卷积算法解调的实际相位做 差运算，判断实际解调相位是否存在跳变点，如果存在跳变点需要对光的偏振态进行判断，当光的偏振态处于偏振相消时需要对跳变点进行修正，修正方式为以预测相位值代替实际解调相位。
上述技术方案的步骤1中，在偏振不相消的情况下，3×3光纤耦合器三端输出光信号存在120°的相位差，光电探测器探测的3×3光纤耦合器三端输出光信号不会趋于相等，通过对3×3光纤耦合器三端输出光信号的大小判断，选取非偏振相消时的解调相位作为历史样本数据
Figure PCTCN2021070278-appb-000001
上述技术方案的步骤2：利用历史样本数据
Figure PCTCN2021070278-appb-000002
构建解调相位自回归滑动平均模型，所述解调相位自回归滑动平均模型当前时刻的解调相位与历史时刻的解调相位满足下列关系式：
Figure PCTCN2021070278-appb-000003
其中，
Figure PCTCN2021070278-appb-000004
分别为k+1,k,k-1…,k-p+1时刻的解调相位值；e(k+1),e(k),…,e(k-q+1)为白噪声残差序列，代表当前时刻与历史时刻的残差；a n(n＝1,2,…,p)为自回归系数，p为回归阶数，θ m(m＝1,2,…,q)为滑动平均系数，q为滑动平均阶数；
采用赤池信息准则或贝叶斯信息准则确定解调相位自回归滑动平均模型阶数p,q,并利用选取的历史解调相位样本序列
Figure PCTCN2021070278-appb-000005
结合最小二乘估计法，确定解调相位自回归滑动平均模型的自回归系数a n和滑动平均系数θ m，从而确定解调相位自回归滑动平均模型的具体形式。
上述技术方案的步骤3中建立的卡尔曼解调相位预测模型表示为：
Figure PCTCN2021070278-appb-000006
其中，Φ(k)为k时刻的状态向量，Φ(k+1)为k+1时刻的状态向 量，Z(k+1)为k+1时刻的测量向量，w(k)为k时刻的系统噪声向量，v(k+1)为k+1时刻的测量噪声向量，A(k+1,k)为从k时刻到k+1时刻的状态转移矩阵，H(k+1)为k+1时刻预测输出矩阵；
以解调相位
Figure PCTCN2021070278-appb-000007
表示的卡尔曼状态向量Φ(k)为：
令：
Figure PCTCN2021070278-appb-000008
Φ(k)＝[φ 1(k) φ 2(k) … φ p(k)] T    (3)
其中，Φ(k)表示解调相位构建的卡尔曼状态向量，T表示矩阵的转置；
进一步将解调相位自回归滑动平均模型引入到卡尔曼解调相位预测模型，得到卡尔曼解调相位预测模型的状态方程为：
令：e 1(k)＝e(k),e 2(k)＝e(k-1),…,e q+1(k)＝e(k-q+1)
Figure PCTCN2021070278-appb-000009
其中Φ(k+1)，Φ(k)分别为k+1,k时刻的相位状态向量,e(k+1),e(k),e(k-1),…,e(k-q+1)为解调相位自回归滑动平均序列的残差白噪声序列，θ 1,θ 2…,θ q为滑动平均系数；
得到卡尔曼解调相位预测模型的观测方程为：
Z(k+1)＝[1 0 … 0]Φ(k+1)      (5)
通过对比公式(2)与公式(4)(5),确定状态转移矩阵A(k+1,k)和预测 输出矩阵H(k+1)的具体形式，进一步利用卡尔曼解调相位状态方程(4)和观测方程(5)推导出卡尔曼解调相位预测模型递推方程组如下：
Figure PCTCN2021070278-appb-000010
K(k+1)＝P(k+1|k)H T(k+1)·
[H(k+1)P(k+1|k)H T(k+1)] -1     (7)
P(k+1|k)＝A(k+1,k)P(k|k)A T(k+1,k)+Q(k)     (8)
P(k+1|k+1)＝[I-K(k+1)H(k+1)]P(k+1|k)     (9)
Figure PCTCN2021070278-appb-000011
表示对k+1时刻状态向量Φ(k+1)的估计值；K(k+1)为k+1时刻的卡尔曼增益矩阵，Φ(k|k)表示k时刻状态向量的估计，Z(k+1)表示公式(5)中的观测向量，P(k+1|k)表示从k时刻到k+1时刻的单步预测误差协方差矩阵，H T(k+1)表示为k+1时刻预测输出矩阵，P(k|k)表示为k时刻预测误差协方差矩阵，A T(k+1,k)表示从k时刻到k+1时刻的状态转移矩阵，T表示转置，P(k+1|k)表示从k时刻到k+1时刻的单步预测误差协方差矩阵，P(k+1|k+1)为k+1时刻预测的误差协方差矩阵，Q(k)是关于w(k)的协方差矩阵，该协方差矩阵可以通过式(1)中残差白噪声序列计算获得，I为单位矩阵。
由于相位解卷积算法是积分式的，即卷积相位展开所叠加的错误补偿值会一直存在后续的相位解卷积结果中，在修正错误补偿相位后，为了消除相位解卷积算法错误补偿的累积性对后续预测值准确性的影响，需要对观测向量Z(k+1)进行修正，即加上一个累加量C(k+1)。
上述技术方案的步骤4中，利用建立的卡尔曼解调相位预测模型，根据历史统计信息和k时刻的解调相位预测k+1时刻的解调相位，即
Figure PCTCN2021070278-appb-000012
将预测值与实际解调值做差运算，判断实际解调相位是否存在跳变点，如果存在跳变点需要 对光的偏振态进行判断，当光的偏振态处于偏振相消时需要对跳变点进行修正，修正方式为以相位预测值代替实际解调相位。
上述技术方案的所述步骤1中，步骤1：选取非偏振相消时的解调相位作为历史样本数据
Figure PCTCN2021070278-appb-000013
Figure PCTCN2021070278-appb-000014
I n(n＝1,2,3)为马赫增德干涉仪的光电探测器探测到的3×3耦合器三端输出光强值，其中A n为直流分量，B n为交流分量，
Figure PCTCN2021070278-appb-000015
为需要解调的相位值，当两束干涉光偏振态接近于正交时，3×3耦合器三端输出光强的交流分量B n趋近于0，导致3×3耦合器三端输出光强I 1≈I 2≈I 3，因此可以通过3×3耦合器三端输出光强对两束干涉光偏振态进行判断，从而选取非偏振相消时的解调相位作为历史样本数据
Figure PCTCN2021070278-appb-000016
上述技术方案的所述步骤2中，利用赤池信息准则或贝叶斯信息准则确定解调相位自回归滑动平均模型阶数的具体方法为：
赤池信息准则对解调相位自回归滑动平均模型定阶为ARMA(p,q),其中p,q满足以下关系式；
Figure PCTCN2021070278-appb-000017
贝叶斯信息准则对解调相位自回归滑动平均模型定阶为ARMA(p,q)，其中p,q满足以下关系式；
Figure PCTCN2021070278-appb-000018
min AIC为赤池信息准则对应的最合适的解调相位自回归滑动平均模型阶数，min BIC为贝叶斯信息准则对应的最合适的解调相位自回归滑动平均模型阶数，式中n为选取作为样本的解调相位
Figure PCTCN2021070278-appb-000019
的数量，
Figure PCTCN2021070278-appb-000020
为模型白噪声方差的估计。
利用历史解调相位样本序列
Figure PCTCN2021070278-appb-000021
并结合最小二乘估计法确定解调相位自回归滑动平均模型的参数a n(n＝1,2,…,p),θ m(m＝1,2,…,q)，从而确定解调相位自回归滑动平均模型的具体形式。
上述步骤2中利用选取历史解调相位样本序列建立ARMA模型要求选择的样本序列
Figure PCTCN2021070278-appb-000022
为平稳序列，因此首先需要利用图检验 法对
Figure PCTCN2021070278-appb-000023
进行平稳性检测，若序列满足平稳性的条件，则直接利用样本序列
Figure PCTCN2021070278-appb-000024
建立ARMA模型。若不满足平稳性条件，则对样本序列
Figure PCTCN2021070278-appb-000025
进行差分运算，直到满足平稳性条件，再将差分后的平稳序列建立ARMA模型。
上述技术方案的步骤4中，用创建的卡尔曼解调相位预测模型，对解调相位数据进行实时预测，并与利用反正切算法和相位解卷积算法解调的实际相位做差运算，如果差值的绝对值大于阈值，则存在跳变点。阈值的选择根据解调系统的噪声水平而定，设定为过去一段时间的不含振动信号的解调相位的方差。偏振相消状态通过ADC(数据采集卡)采集的3×3光纤耦合器三端输出的光强信号进行判断，具体地，对三路光强信号两两做差运算获得三组差值，若三组差值均小于设定的阈值，即判断为偏振相消状态。
上述步骤4中偏振相消状态的判断方法为分析系统获得的3×3耦合器输出光强信号I 1,I 2,I 3。
进一步，令S 1＝|I 1-I 2|,S 2＝|I 2-I 3|,S 1＝|I 1-I 3|
当[(S 1<N)∩(S 2<N)∩(S 3<N)]＝TRUE，判断当前光路中进行干涉的两束光偏振态接近正交，反之不成立。式中N表示对ADC采集的3×3耦合器输出光强数据噪声水平估计。
根据跳变存在判断结果和偏振状态判断结果，对实际解调相位Φ_R(k+1)进行修正，以预测相位代替实际解调相位。
相位解卷积算法中卷积相位展开所叠加的错误补偿会一直存在后续相位解卷积结果中，为了保证卡尔曼解调相位预测模型后续预测相位的正确性，对量测状态向量的修正C(k+1)应该是相位修正量的累积结果，即C(k+1)＝C(k)+M(k),M(k)为预测值与实际解调值之间的差值。
本发明解决了光纤振动解调系统中由于偏振诱导衰落导致解调相位存在随机阶跃跳变的问题，保证了后续的基于振动数据分析的正确性。
本说明书未作详细描述的内容属于本领域专业技术人员公知的现有技术。

Claims (9)

  1. 一种光纤相位解调中偏振诱导衰落导致相位跳变修正方法，其特征在于，它包括如下步骤：
    步骤1：通过对马赫增德干涉仪中3×3光纤耦合器三端输出光信号分析选取偏振不相消时的解调相位作为历史样本数据；
    步骤2：利用步骤1选择的历史样本序列，采用时间序列分析方法构建解调相位自回归滑动平均模型，利用赤池信息准则或贝叶斯信息准则确定解调相位自回归滑动平均模型阶数，并利用最小二乘估计法确定解调相位自回归滑动平均模型的自回归系数和滑动平均系数；
    步骤3：以解调相位表示卡尔曼状态向量，并利用步骤2中获得的解调相位自回归滑动平均模型初始化卡尔曼状态转移矩阵、系统噪声向量、预测输出矩阵等参数，建立卡尔曼解调相位预测模型，推导卡尔曼解调相位预测模型递推方程组；
    步骤4：用创建的卡尔曼解调相位预测模型，对解调相位进行实时预测，并与利用反正切算法和相位解卷积算法解调的实际相位做差运算，判断实际解调相位是否存在跳变点，如果存在跳变点需要对光的偏振态进行判断，当光的偏振态处于偏振相消时需要对跳变点进行修正，修正方式为以预测相位值代替实际解调相位值。
  2. 根据权利要求1所述的光纤相位解调中偏振诱导衰落导致相位跳变修正方法，其特征在于：所述步骤1中，在偏振不相消的情况下，3×3光纤耦合器三端输出光信号存在120°的相位差，光电探测器探测3×3光纤耦合器三端输出光信号不会趋于相等，通过对3×3光纤耦合器三端输出光信号的大小判断，选取非偏振相消时的解调相位作为历史样本数据
    Figure PCTCN2021070278-appb-100001
  3. 根据权利要求1所述的光纤相位解调中偏振诱导衰落导致相位跳变修正方法，其特征在于：步骤2：利用历史样本数据
    Figure PCTCN2021070278-appb-100002
    构建解调相位自回归滑动平均模型，所述解调相位自回归滑动平均模型当前时刻的解调相位与历史时刻的解调相位满足下列关系式：
    Figure PCTCN2021070278-appb-100003
    其中，
    Figure PCTCN2021070278-appb-100004
    分别为k+1,k,k-1…,k-p+1时刻的解调相位值；e(k+1),e(k),…,e(k-q+1)为白噪声残差序列，代表当前时刻与历史时刻的残差，a n(n＝1,2,…,p)为自回归系数，p为回归阶数，θ m(m＝1,2,…,q)为滑动平均系数，q为滑动平均阶数；
    采用赤池信息准则或贝叶斯信息准则确定解调相位自回归滑动平均模型阶数p,q,并利用选取的历史解调相位样本序列
    Figure PCTCN2021070278-appb-100005
    结合最小二乘估计法，确定解调相位自回归滑动平均模型的自回归系数a n和滑动平均系数θ m，从而确定解调相位自回归滑动平均模型的具体形式。
  4. 根据权利要求1所述的光纤相位解调中偏振诱导衰落导致相位跳变修正方法，其特征在于：步骤3中建立的卡尔曼解调相位预测模型表示为：
    Figure PCTCN2021070278-appb-100006
    其中，Φ(k)为k时刻的状态向量，Φ(k+1)为k+1时刻的状态向量，Z(k+1)为k+1时刻的测量向量，w(k)为k时刻的系统噪声向量，v(k+1)为k+1时刻的测量噪声向量，A(k+1,k)为从k时刻到k+1时刻的状态转移矩阵，H(k+1)为k+1时刻预测输出矩阵；
    以解调相位
    Figure PCTCN2021070278-appb-100007
    表示的卡尔曼状态向量Φ(k)为：
    令：
    Figure PCTCN2021070278-appb-100008
    Φ(k)＝[φ 1(k) φ 2(k) … φ p(k)] T  (3)
    其中，Φ(k)表示解调相位构建的卡尔曼状态向量，T表示矩阵的转置；
    进一步将解调相位自回归滑动平均模型引入到卡尔曼解调相位预测模型，得到卡尔曼解调相位预测模型的状态方程为：
    令：e 1(k)＝e(k),e 2(k)＝e(k-1),…,e q+1(k)＝e(k-q+1)
    Figure PCTCN2021070278-appb-100009
    其中Φ(k+1)，Φ(k)分别为k+1,k时刻的相位状态向量，e(k+1),e(k),e(k-1),…,e(k-q+1)为解调相位自回归滑动平均序列的残差白噪声序列，θ 1,θ 2…,θ q为滑动平均系数；
    得到卡尔曼解调相位预测模型的观测方程为：
    Z(k+1)＝[1 0 … 0]Φ(k+1)  (5)
    通过对比公式(2)与公式(4)(5),确定状态转移矩阵A(k+1,k)和预测输出矩阵H(k+1)的具体形式，进一步利用卡尔曼解调相位状态方程(4)和观测方程(5)推导出卡尔曼解调相位预测模型递推方程组如下：
    Figure PCTCN2021070278-appb-100010
    Figure PCTCN2021070278-appb-100011
    P(k+1|k)＝A(k+1,k)P(k|k)A T(k+1,k)+Q(k)  (8)
    P(k+1|k+1)＝[I-K(k+1)H(k+1)]P(k+1|k)  (9)
    Figure PCTCN2021070278-appb-100012
    表示对k+1时刻状态向量Φ(k+1)的估计值；K(k+1)为k+1时刻的卡尔曼增益矩阵，Φ(k|k)表示k时刻状态向量的估计，Z(k+1)表示公式(5)中的观测向量，P(k+1|k)表示从k时刻到k+1时刻单步预测误差协方差矩阵，H T(k+1)表示为k+1时刻预测输出矩阵，P(k|k)表示为k时刻预测误差协方差矩阵，A T(k+1,k)表示从k时刻到k+1时刻的状态转移矩阵，加T表示转置，P(k+1|k)表示从k时刻到k+1时刻的单步预测误差协方差矩阵，P(k+1|k+1)为k+1时刻预测的误差协方差矩阵，Q(k)是关于w(k)的协方差矩阵，该协方差矩阵通过式(1)中残差白噪声序列计算获得，I为单位矩阵；
    由于相位解卷积算法是积分式的，即卷积相位展开所叠加的错误补偿值会一直存在后续的相位解卷积结果中，在修正错误补偿相位后，为了消除相位解卷积算法错误补偿的累积性对后续预测值准确性的影响，需要对观测向量Z(k+1)进行修正，即加上一个累加量C(k+1)。
  5. 根据权利要求1所述的光纤相位解调中偏振诱导衰落导致相位跳变修正方法，其特征在于：步骤4中，利用建立的卡尔曼解调相位预测模型，根据历史统计信息和k时刻的解调相位预测k+1时刻的解调相位，即
    Figure PCTCN2021070278-appb-100013
    将预测值与实际解调值做差运算，判断实际解调相位是否存在跳变点，如果存在跳变点需要对光的偏振态进行判断，当光的偏振态处于偏振相消时需要对跳变点进行修正，修正方式为以预测相位代替实际解调相位。
  6. 根据权利要求1所述的光纤相位解调中偏振诱导衰落导致相位跳变修正方法，其特征在于：所述步骤1中，步骤1：选取非偏振相消时的解调相位作为历史样本数据
    Figure PCTCN2021070278-appb-100014
    Figure PCTCN2021070278-appb-100015
    I n(n＝1,2,3)为马赫增德干涉仪的光电探测器探测到的3×3耦合器三端输出光强值，其中A n为直流分量，B n为交流分量，
    Figure PCTCN2021070278-appb-100016
    为需要解调的相位值，当两束干涉光偏振态接近于正交时，3×3耦合器三端输出光强的交流分量B n趋近于0，导致3×3耦合器三端输出光强I 1≈I 2≈I 3，因此可以通过3×3耦合器三端输出光强对两束干涉光偏振态进行判断，从而选取非偏振相消时的解调相位作为历史样本数据
    Figure PCTCN2021070278-appb-100017
  7. 根据权利要求3所述的光纤相位解调中偏振诱导衰落导致相位跳变修正方法，其特征在于：所述步骤2中，利用赤池信息准则或贝叶斯信息准则确定解调相位自回归滑动平均模型阶数的具体方法为：
    赤池信息准则对解调相位自回归滑动平均模型定阶为ARMA(p,q),其中p,q满足以下关系式；
    Figure PCTCN2021070278-appb-100018
    贝叶斯信息准则对解调相位自回归滑动平均模型定阶为ARMA(p,q)，其中p,q满足以下关系式；
    Figure PCTCN2021070278-appb-100019
    min AIC为赤池信息准则对应的最合适的解调相位自回归滑动平均模型阶数，min BIC为贝叶斯信息准则对应的最合适的解调相位自回归滑动平均模型阶数，式中n为选取作为样本的解调相位
    Figure PCTCN2021070278-appb-100020
    的数量，
    Figure PCTCN2021070278-appb-100021
    为模型白噪声方差的估计。
  8. 根据权利要求7所述的光纤相位解调中偏振诱导衰落导致相位跳变修正方法，其特征在于：利用历史解调相位样本序列
    Figure PCTCN2021070278-appb-100022
    结合最小二乘估计法确定解调相位自回归滑动平均模型的参数a n(n＝1,2,…,p),θ m(m＝1,2,…,q)，从而确定解调相位自回归滑动平均模型具体形式。
  9. 根据权利要求1所述的光纤相位解调中偏振诱导衰落导致相位跳变修正方法，其特征在于：所述步骤4中，用创建的卡尔曼解调相位预测模型，对解调相位数据进行实时预测，并与利用反正切 算法和相位解卷积算法解调的实际相位做差运算，如果差值的绝对值大于阈值，则存在跳变点。
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