电力系统频率测量及其在数字语音真伪鉴别中的应用
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摘要
频率反映发电和负荷之间的动态平衡，是电力系统最基本的参数之一，准确快速的频率测量对电力系统运行、监测和控制具有重要的意义。频率波动不仅表征系统的动态行为而且包含丰富的时间信息，其变化具有均一性和独特性。利用这一特点，电网频率准则(Electric Network Frequency Criterion, ENF)将电网频率引入数字语音证据的真实性与完整性检测。本文研究电力系统频率测量方法，在北美电网频率监测系统FNET的基础上，将电力系统频率测量数据用于数字语音信号的真伪鉴别。
在介绍FNET框架的基础上，推导用于第二代频率扰动记录单元(FrequencyDisturbance Recorder,FDR)的递归式离散傅立叶变换(Discrete Fourier Transform,DFT)算法，FDR算法引入信号再采样策略，根据频率估计的初值逐点校正数据窗内的电压采样点，确保在每个周期内的采样点数目保持不变，使得实际采样满足同步采样条件，达到提高频率和电压相量估计精度的目的。仿真结果表明FDR算法抑制噪声和谐波干扰的能力强、具有良好的稳态性能和动态频率跟踪能力；降低相角估计误差中的正弦误差项是进一步提高FDR算法精度的有效途径，提高电压信号的采样率、增加相角的多项式拟合阶数和FDR硬件装置中A/D转换器的字长并不从根本上改善FDR算法精度。
提出一种改进的电网频率估计算法，引入采样点间隔参数k，采用四个间距为k的采样点建立电压采样点与频率之间的数学关系，根据最小二乘原理得出频率估计的表达式，分别考虑白噪声和谐波的影响，推导出频率估计的近似显性表达式。采样点间隔参数影响频率估计精度，当信号的圆周频率与采样点间隔参数的乘积取π3时，算法具有最佳的白噪声和三次谐波抑制能力。仿真得出的最佳采样点间隔和理论值一致；算法的精度在稳态接近FDR算法，但动态跟踪能力优于FDR算法。该方法不借助数学优化算法或迭代过程即可估计电网频率，所需的采样点数目少、运算速度快、响应时间短，适合短时间窗条件下的频率估计。
将电网频率测量数据用于数字语音真伪鉴别，提出一套完整的数字语音真伪鉴别流程。采用稳健统计方法辨识FDR原始数据中的尖峰值，引入B样条基函数，通过B样条基函数的线性组合重构FDR原始数据，达到消除缺失数据段和尖峰值的目的，构建用于真伪鉴别的大型标准电网频率数据库；提出一种振荡器误差校正算法，引入数值偏差和时间间隔偏差两个参数，采用递推方式校正ENF估计值序列和电网频率子序列，解决现有的ENF序列无法与电网标准频率直接比较的问题；改进短时傅立叶变换，采用两阶段ENF估计方法，从窗函数、补零操作、噪声干扰、频率偏移量四个方面，给出检验ENF估计子的准确度和精确度的流程。算例表明，文中的ENF估计子不需要窗函数和补零操作且近似于无偏估计，在减少运算量的同时能获得满意的频率估计效果。通过电网频率数据库匹配确定数字语音记录的制作时间并实例验证该真伪鉴别流程的正确性。
引入相位估计鉴别数字语音信号的真伪。考虑DFT结果中负频率分量的影响，得出一种正弦信号相位的高精度估计公式；在信号导数法估计频率的基础上，根据导数信号的相位推导出原始正弦信号的相位估计表达式。算例表明，相位是检测数字语音信号真伪的另一个有效特征量，文中两种相位估计算法均能在篡改点附近检测出估计值不同程度的突变，通过估计值的变化率即可判断数字语音记录是否被修改过。
Frequency is one of the fundamental parameters of power system since it canfaithfully reflect the dynamic behavior of system generation and load. Fast and accuratefrequency estimation plays a critical role in system operation, monitoring and control.Frequency variation not only embodies system’s dynamic behaviors but contains plentyof time information. From different time scales, the variation is uniform and unique.The electric network frequency criterion (ENF) makes good use of this feature byincorporating power system frequency with forensic digital audio authentication (DAA).This paper analyzes power system frequency measurement methods and then applies thefrequency measurements in DAA on the basis of the North American power systemfrequency monitoring system FNET.
Based on brief introduction of the FNET system, recursive discrete Fouriertransform (DFT) used in the second generation of frequency disturbance recorder (FDR)is deduced followed by a re-sampling strategy. The re-sampling strategy adjusts eachdata sample in one data window according to the coarse estimation given by therecursive DFT. It guarantees that the number of sample points within one cycle remainsconstant regardless of frequency change of a real voltage signal; hence, the sampling isnearly a synchronized sampling and as a consequence the frequency and voltage phasorcan be estimated accurately. Simulation results indicate that the FDR algorithm is robustto white noise and harmonics, and that the frequency tracking ability in static anddynamic condition is excellent. Further improvement of the accuracy of the FDRalgorithm lies in reduction of sinusoidal term in the phase angle estimation error,whereas the increase of sampling frequency, polynomial fitting order of phase anglesand word length of the A/D converter do not necessarily refine the accuracy.
An improved frequency estimation algorithm is proposed using least squaremethod. A sampling interval parameter k is introduced, and four neighboring sampleswith interval k are adopted to establish the mathematic relationship between voltagesamples and system frequency. Noise and harmonics are considered separately whichhelps to deduce the final explicit formula for frequency estimation. The samplinginterval is the key parameter of this algorithm, and its optimal value is obtained if theproduction of signal radian frequency and sapling interval equals to π3. If thiscondition is met during estimation, the algorithm will then possess the best performance of noise and3rd-harmonics suppression. Simulation results validate this theoretical value;the performance of this proposed method is close to that of the FDR algorithm in staticscenarios, but has better frequency tracking ability. It can estimate frequency withoutiteration, and needs a few sampling points; hence, the frequency is measured in a fastermanner with a shorter time delay, which implies that the proposed method is suitable forfast frequency estimation of a short data window.
An entire procedure of DAA is proposed. Robust statistical method is introduced toidentify the spikes contained in FDR raw data, and a series of B-spline basis functionsare used to replace the missing segments; an ad hoc standard power system frequencydatabase for DAA is then established when outliers are removed. An iterative oscillatorerror correction algorithm is proposed by introducing value offset and time intervaloffset, and this method overcomes mismatch problem of the extracted ENF sequenceagainst the FDR data. A two-step method for ENF estimation is used by adjusting thecurrent short-time Fourier transform. To learn the accuracy and precision of any ENFestimator, a procedure considering windowing function, zero-padding factor, noisyinfluence and frequency bin offset is proposed. Testing results indicate that the ENFestimator in this paper needs neither windowing function nor zero-padding factor, and isnearly an unbiased estimator, which avoids the intensive computation withoutcompromising the accuracy. Determination of production time of an audio recording istested by frequency database matching and the entire authentication procedure isvalidated by case studies.
Phase estimation is introduced as an alternative method for DAA. Considering thenegative frequency component of the DFT output, a phase angle estimation method withhigh precision is deduced. Based on the signal derivative method for frequencyestimation, another phase estimation method using phase angle of derivative signal isproposed. Massive testing indicates that the phase information is an effective feature forthe DAA, and that the two methods can detect change near the tampering points. Bychecking the rate of change of phase sequence the tampering points can be located then.
在介绍FNET框架的基础上，推导用于第二代频率扰动记录单元(FrequencyDisturbance Recorder,FDR)的递归式离散傅立叶变换(Discrete Fourier Transform,DFT)算法，FDR算法引入信号再采样策略，根据频率估计的初值逐点校正数据窗内的电压采样点，确保在每个周期内的采样点数目保持不变，使得实际采样满足同步采样条件，达到提高频率和电压相量估计精度的目的。仿真结果表明FDR算法抑制噪声和谐波干扰的能力强、具有良好的稳态性能和动态频率跟踪能力；降低相角估计误差中的正弦误差项是进一步提高FDR算法精度的有效途径，提高电压信号的采样率、增加相角的多项式拟合阶数和FDR硬件装置中A/D转换器的字长并不从根本上改善FDR算法精度。
提出一种改进的电网频率估计算法，引入采样点间隔参数k，采用四个间距为k的采样点建立电压采样点与频率之间的数学关系，根据最小二乘原理得出频率估计的表达式，分别考虑白噪声和谐波的影响，推导出频率估计的近似显性表达式。采样点间隔参数影响频率估计精度，当信号的圆周频率与采样点间隔参数的乘积取π3时，算法具有最佳的白噪声和三次谐波抑制能力。仿真得出的最佳采样点间隔和理论值一致；算法的精度在稳态接近FDR算法，但动态跟踪能力优于FDR算法。该方法不借助数学优化算法或迭代过程即可估计电网频率，所需的采样点数目少、运算速度快、响应时间短，适合短时间窗条件下的频率估计。
将电网频率测量数据用于数字语音真伪鉴别，提出一套完整的数字语音真伪鉴别流程。采用稳健统计方法辨识FDR原始数据中的尖峰值，引入B样条基函数，通过B样条基函数的线性组合重构FDR原始数据，达到消除缺失数据段和尖峰值的目的，构建用于真伪鉴别的大型标准电网频率数据库；提出一种振荡器误差校正算法，引入数值偏差和时间间隔偏差两个参数，采用递推方式校正ENF估计值序列和电网频率子序列，解决现有的ENF序列无法与电网标准频率直接比较的问题；改进短时傅立叶变换，采用两阶段ENF估计方法，从窗函数、补零操作、噪声干扰、频率偏移量四个方面，给出检验ENF估计子的准确度和精确度的流程。算例表明，文中的ENF估计子不需要窗函数和补零操作且近似于无偏估计，在减少运算量的同时能获得满意的频率估计效果。通过电网频率数据库匹配确定数字语音记录的制作时间并实例验证该真伪鉴别流程的正确性。
引入相位估计鉴别数字语音信号的真伪。考虑DFT结果中负频率分量的影响，得出一种正弦信号相位的高精度估计公式；在信号导数法估计频率的基础上，根据导数信号的相位推导出原始正弦信号的相位估计表达式。算例表明，相位是检测数字语音信号真伪的另一个有效特征量，文中两种相位估计算法均能在篡改点附近检测出估计值不同程度的突变，通过估计值的变化率即可判断数字语音记录是否被修改过。
Frequency is one of the fundamental parameters of power system since it canfaithfully reflect the dynamic behavior of system generation and load. Fast and accuratefrequency estimation plays a critical role in system operation, monitoring and control.Frequency variation not only embodies system’s dynamic behaviors but contains plentyof time information. From different time scales, the variation is uniform and unique.The electric network frequency criterion (ENF) makes good use of this feature byincorporating power system frequency with forensic digital audio authentication (DAA).This paper analyzes power system frequency measurement methods and then applies thefrequency measurements in DAA on the basis of the North American power systemfrequency monitoring system FNET.
Based on brief introduction of the FNET system, recursive discrete Fouriertransform (DFT) used in the second generation of frequency disturbance recorder (FDR)is deduced followed by a re-sampling strategy. The re-sampling strategy adjusts eachdata sample in one data window according to the coarse estimation given by therecursive DFT. It guarantees that the number of sample points within one cycle remainsconstant regardless of frequency change of a real voltage signal; hence, the sampling isnearly a synchronized sampling and as a consequence the frequency and voltage phasorcan be estimated accurately. Simulation results indicate that the FDR algorithm is robustto white noise and harmonics, and that the frequency tracking ability in static anddynamic condition is excellent. Further improvement of the accuracy of the FDRalgorithm lies in reduction of sinusoidal term in the phase angle estimation error,whereas the increase of sampling frequency, polynomial fitting order of phase anglesand word length of the A/D converter do not necessarily refine the accuracy.
An improved frequency estimation algorithm is proposed using least squaremethod. A sampling interval parameter k is introduced, and four neighboring sampleswith interval k are adopted to establish the mathematic relationship between voltagesamples and system frequency. Noise and harmonics are considered separately whichhelps to deduce the final explicit formula for frequency estimation. The samplinginterval is the key parameter of this algorithm, and its optimal value is obtained if theproduction of signal radian frequency and sapling interval equals to π3. If thiscondition is met during estimation, the algorithm will then possess the best performance of noise and3rd-harmonics suppression. Simulation results validate this theoretical value;the performance of this proposed method is close to that of the FDR algorithm in staticscenarios, but has better frequency tracking ability. It can estimate frequency withoutiteration, and needs a few sampling points; hence, the frequency is measured in a fastermanner with a shorter time delay, which implies that the proposed method is suitable forfast frequency estimation of a short data window.
An entire procedure of DAA is proposed. Robust statistical method is introduced toidentify the spikes contained in FDR raw data, and a series of B-spline basis functionsare used to replace the missing segments; an ad hoc standard power system frequencydatabase for DAA is then established when outliers are removed. An iterative oscillatorerror correction algorithm is proposed by introducing value offset and time intervaloffset, and this method overcomes mismatch problem of the extracted ENF sequenceagainst the FDR data. A two-step method for ENF estimation is used by adjusting thecurrent short-time Fourier transform. To learn the accuracy and precision of any ENFestimator, a procedure considering windowing function, zero-padding factor, noisyinfluence and frequency bin offset is proposed. Testing results indicate that the ENFestimator in this paper needs neither windowing function nor zero-padding factor, and isnearly an unbiased estimator, which avoids the intensive computation withoutcompromising the accuracy. Determination of production time of an audio recording istested by frequency database matching and the entire authentication procedure isvalidated by case studies.
Phase estimation is introduced as an alternative method for DAA. Considering thenegative frequency component of the DFT output, a phase angle estimation method withhigh precision is deduced. Based on the signal derivative method for frequencyestimation, another phase estimation method using phase angle of derivative signal isproposed. Massive testing indicates that the phase information is an effective feature forthe DAA, and that the two methods can detect change near the tampering points. Bychecking the rate of change of phase sequence the tampering points can be located then.
引文
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