A numerical integration method for autonomously eliminating zero-point drift of pulse signals

Abstract

The present invention aims to solve the problem of poor versatility or zero-point drift caused by the presence of background noise in oscilloscope sampling, which accumulates continuously during the numerical integration process, leading to distortion of the integrated waveform. The present invention provides a numerical integration method for autonomously eliminating zero-point drift of pulse signals. The present invention eliminates the DC component and random component in the oscilloscope background noise in stages. First, a random array is defined and assigned to the sampling results of the DC component in the oscilloscope background noise, thereby maintaining an integer multiple relationship between the signal and the oscilloscope vertical resolution d0. Second, by analyzing the characteristic parameters of the integrated signal and its distribution, data processing is performed to obtain a discrete signal after random component elimination. This eliminates the need for manual identification of the starting and ending points of the signal, thereby perfectly retaining the pulse signal monitored by the oscilloscope.

Description

Technical Field

[0001] The present invention relates to the field of signal numerical processing, and in particular to a numerical integration method for autonomously eliminating zero-point drift of a pulse signal. Background Art

[0002] Differential voltage and current probes are often used to measure the voltage and current of high-voltage pulses in pulse power devices. The obtained differential signal can be restored by an integrator or numerical integration.

[0003] In current engineering, differential signals are typically restored using an integrator, which is then acquired and displayed by a digital oscilloscope. However, different integrator parameters are required for signals with varying leading edges and pulse widths, making this approach less universal. Furthermore, obtaining integrator performance parameters requires carefully designed calibration experiments, which typically use numerical integration as a reference standard. Therefore, using an integrator introduces greater measurement errors than numerical integration.

[0004] Numerical integration signal restoration involves directly acquiring a differential signal with an oscilloscope and then restoring the signal through numerical calculation. This method theoretically offers excellent versatility and accuracy. However, due to the inherent noise floor of the oscilloscope's sampling, this noise accumulates during the numerical integration process, causing distortion in the integrated waveform and severely affecting measurement accuracy. This phenomenon is known as zero drift.

[0005] The phenomenon of background noise is that when the oscilloscope input signal is zero, the output signal is non-zero; instead, it is a random noise segment, known as the background noise. Numerically, the expected value of the background noise is generally not zero. Therefore, the background noise of an oscilloscope can be considered to consist of a DC component ε and a random component η, which is expected to be zero. The DC component ε causes the numerically integrated waveform to vary linearly over time, while the random component η superimposes low-frequency oscillations on the numerically integrated waveform.

[0006] The noise floor is primarily generated by three factors. The first is thermal error, which is caused by temperature fluctuations and changes in circuit component parameters during oscilloscope operation. The second is quantization error, which is introduced by approximating analog signals to digital signals during the oscilloscope's analog-to-digital conversion process. The third is random interference, including power grid fluctuations, electromagnetic interference in space, and mutual interference between oscilloscope channels. Within the noise floor, the DC component ε is primarily determined by thermal error, while the random component η is primarily determined by quantization error and random factors.

[0007] In order to solve the zero drift problem in numerical integration, the average value method is currently generally used to eliminate the background noise. This method requires sampling a sufficiently long background signal before the oscilloscope detects the input signal and calculating the average value μ of this signal, that is:

[0008]

[0009] In equation (1), s(n) is the discrete signal sampled by the oscilloscope, and n0 is the length of the background signal. Since the signal's average value μ is the maximum likelihood estimate of the parameter ε, the average value μ can be equated to the DC component ε of the background noise. Equation (2) is used to eliminate the influence of the DC component ε on the integration result. In equation (2), the discrete signal s1(n) is the discrete signal s(n) after the influence of the DC component ε is eliminated, the integrated signal S1(n) is the numerical integration result of the discrete signal s1(n), and t0 is the sampling interval of the oscilloscope.

[0010]

[0011] Although the average value method can effectively eliminate the influence of the DC component ε on numerical integration, there is currently no feasible method to effectively remove the random component η. The influence of the random component η on the integral signal S1 cannot be ignored. The low-frequency interference introduced by the random component η will cause significant difficulties in the amplitude and leading edge reading of the integral signal S1.

[0012] Secondly, signal processing using the averaging method requires manual intervention. This method requires identifying the starting point of the input signal being monitored by the oscilloscope and capturing the background signal before the input signal begins for data processing. However, in pulsed power devices, the monitored signal often has a low-amplitude pre-pulse, making it difficult to determine the signal's starting point. Therefore, manual identification of the input signal's starting point is generally required. As pulsed power devices scale up, the number of monitored signals can reach hundreds, making manual operation a significant engineering inconvenience.

[0013] Furthermore, using the average value method to process signals can alter their primary characteristics. In equation (2), s(n) represents the digital signal sampled by the oscilloscope, and its value is an integer multiple of the oscilloscope's vertical resolution d0. However, the statistically average value μ of the signal does not have an integer multiple relationship with the oscilloscope's vertical resolution d0. After processing the equations, the discrete signal s1(n) also loses its integer multiple relationship with the oscilloscope's vertical resolution d0, which makes it difficult to subsequently eliminate the influence of η. Summary of the Invention

[0014] The purpose of the present invention is to solve the problem that the existing method of using an integrator or numerical integration to restore the signal to achieve the measurement of the voltage and current of the high-voltage pulse has poor versatility or the background noise exists due to the sampling of the oscilloscope, which accumulates continuously during the numerical integration process, resulting in the distortion of the integrated waveform and the resulting zero drift phenomenon. A numerical integration method is provided to autonomously eliminate the zero drift of the pulse signal.

[0015] In order to achieve the above object, the technical solution adopted by the present invention is:

[0016] A numerical integration method for autonomously eliminating zero-point drift of a pulse signal is characterized in that it includes the following steps:

[0017] Step 1: Use a differential probe to measure the pulse signal X0(t) to obtain the differential monitoring signal x(t) of the pulse to be measured;

[0018] Step 2: Set the oscilloscope sampling parameters, including sampling interval t0, sampling length T0, and vertical resolution d0;

[0019] Step 3: Use an oscilloscope to sample the differential monitoring signal x(t) to obtain a discrete signal s(n). The discrete signal s(n) contains the discrete differential monitoring signal x(n) and the corresponding DC component ε(n) in the background noise and the random component η(n) in the background noise.

[0020] s(n)=x(n)+ε(n)+η(n),n∈[1,n f ]

[0021] Among them, n is the sequence number of the sampling point, n f is the total number of sampling points, n f =T0 / t0,n f , n are both integers;

[0022] Step 4: Based on the sampling interval t0, the discrete signal s(n) is numerically integrated to obtain a discrete integral signal S(n);

[0023]

[0024] Step 5: Calculate the true value estimate ε0 of the DC component array ε(n) in the background noise;

[0025] Step 6, assign values to the DC component array ε(n) so that the average value of the DC component array ε(n) is the true value estimate ε0;

[0026] Step 7: Eliminate the influence of the DC component ε(n) in the background noise of the discrete signal s(n) on the numerical integration, and obtain the discrete signal s1(n) after the DC component is eliminated;

[0027] s1(n)=s(n)-ε(n), n∈[1,n f ]

[0028] Step 8: Eliminate the influence of the random component η in the background noise of the discrete signal s1(n) on the numerical integration, and obtain the discrete signal s2(n) after the random component is eliminated;

[0029] Step 9: Perform numerical integration on the discrete signal s2(n) to obtain the integrated signal S2(n) after eliminating the zero drift:

[0030]

[0031] Furthermore, step 5 is specifically as follows:

[0032] 5.1, based on the last sampling moment X(n f ) has a zero amplitude and the expectation of the random component η is zero, and the discrete integral signal S(n f ):

[0033]

[0034] 5.2. Calculate the true value estimate ε0 of the DC component array ε(n) in the background noise:

[0035] ε0=S(n f ) / (n f ·t0).

[0036] Furthermore, step 6 is specifically as follows:

[0037] 6.1. Determine the range of the true value estimate ε0

[0038]

[0039] Wherein, h is the result of rounding down the ratio of the estimated true value of the DC component ε0 to the vertical resolution d0 of the oscilloscope;

[0040] 6.2. Calculate the number n of DC component arrays ε(n) with the value hd0 h :

[0041]

[0042] 6.3. The array ε(n) has a total of n f elements, randomly select n of them h The first element is assigned the value hd0, and the remaining array elements are assigned the value (h+1)d0, so that the average value of the array ε(n) is the true value estimate ε0.

[0043] Furthermore, in step 1, the time integral signal X(t) of the differential monitoring signal x(t) is:

[0044]

[0045] Define the amplitudes of the pulse signal X0(t) to be measured and the integrated signal X(t) to be U0 and U respectively; the leading edge time of the pulse signal X0(t) to be measured is t r; The signal length of the pulse signal X0(t) to be measured is T;

[0046] The sensitivity of the differential probe is K=U / U0;

[0047] In step 2, the sampling interval t0 satisfies: t0≤t r / M; the sampling length T0 satisfies: T0≥T; the vertical resolution d0 satisfies: d0 r );

[0048] Among them, M and P are sampling coefficient and quantization coefficient respectively.

[0049] Furthermore, step 8 is specifically as follows:

[0050] 8.1. Calculate the coefficient m of the characteristic parameter:

[0051]

[0052] 8.2. Calculate the characteristic parameter k(n) of the discrete signal s1(n):

[0053]

[0054] 8.3. Set the threshold Q and assign a value to the discrete signal s1(n) according to the characteristic parameter k(n): when k(n) ≤ Q, let s2(n) = 0; when k(n) > Q, let s2(n) = s1(n).

[0055] Furthermore, in step 8.1, m≥16.

[0056] Furthermore, in step 8.3, Q=1.3.

[0057] Furthermore, in step 2, M≥20, P=30.

[0058] Compared with the prior art, the present invention has the following beneficial technical effects:

[0059] 1. Compared with existing numerical integration methods, the numerical integration method proposed in the present invention for autonomously eliminating zero-point drift of pulse signals not only eliminates the influence of the DC component in the oscilloscope background noise on the integration result, but also effectively eliminates the random component in the background noise. This method can effectively eliminate the oscilloscope background noise without distorting the measurement results.

[0060] ​2. The numerical integration method for autonomously eliminating zero-point drift of pulse signals proposed in the present invention is different from the existing method that takes the oscilloscope background noise as a constant. The present invention defines the sampling result ε(n) of the DC component in the oscilloscope background noise as a random array whose value is hd0 or (h+1)d0, where h is the result of rounding down ε0 / d0, ε0 is the statistical average value of ε(n), and d0 is the vertical resolution of the oscilloscope. During the signal processing process, the relationship between the signal and the oscilloscope vertical resolution d0 as an integer multiple can be maintained.

[0061] 3. The numerical integration method proposed in this invention for autonomously eliminating pulse signal zero-point drift employs a method for eliminating the random component η of the background noise from a discrete signal s1, after the DC component of the background noise has been removed. This method retains the data points in s1(n) that are related to the oscilloscope monitoring signal x, while setting the data in s1(n) that do not contain the signal x and are only related to η to zero. This method automatically determines whether each data point in s1(n) is related to the oscilloscope monitoring signal x; compared to existing methods, it eliminates the need for manual identification of the starting and ending points of signal x.

[0062] 4. The numerical integration method proposed in this invention for autonomously eliminating pulse signal zero-point drift can effectively eliminate random components from background noise while fully preserving the pulse signal monitored by the oscilloscope. It has been verified that when the monitoring signal x(n) = 0, the probability of eliminating the random component is greater than 80%; when the monitoring signal |x(n)| is equivalent to the oscilloscope's vertical resolution d0, the probability of retaining the monitoring signal x(n) is greater than 0.65; and when the monitoring signal |x(n)| ≥ 2d0, all waveform details of x(n) are fully preserved. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 This is a flow chart of the numerical integration method for autonomously eliminating zero-point drift of a pulse signal according to the present invention;

[0064] Figure 2 Schematic diagram of the differential measurement system used in an embodiment of the present invention;

[0065] Figure 3 : is a normalized waveform diagram of the measurement signal x0 output by the resistor divider in the differential measurement system in an embodiment of the present invention;

[0066] Figure 4 : is a waveform diagram of a discrete signal s obtained by sampling with an oscilloscope in an embodiment of the present invention;

[0067] Figure 5 : is a waveform diagram of an integrated signal S after numerical integration of a discrete signal s in an embodiment of the present invention;

[0068] Figure 6This is a waveform diagram of the discrete integral signal S1 after eliminating the influence of the DC component in an embodiment of the present invention;

[0069] Figure 7 3 is a waveform comparison diagram of the discrete integral signal S2 after further eliminating the influence of random components and the normalized measurement signal x0 output by the resistor divider in an embodiment of the present invention;

[0070] Figure 8 for Figure 7 A partial enlarged view of . DETAILED DESCRIPTION

[0071] To make the objects, advantages, and features of the present invention more clearly apparent, the numerical integration method for autonomously eliminating zero-point drift of a pulse signal proposed by the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood by those skilled in the art that these embodiments are merely intended to explain the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0072] First, define the pulse signal to be measured in the pulse power device as X0(t). Use the differential probe to measure the pulse signal to be measured X0(t). The obtained differential monitoring signal of the pulse to be measured is x(t). Let the integrated signal of the pulse to be measured be X(t), that is:

[0073]

[0074] The amplitudes of the measured pulse signal X0(t) and the integrated signal X(t) are defined as U0 and U, respectively, with units of V and Vs, and the sensitivity of the differential probe is K=U / U0, with units of s.

[0075] Ideally, the pulse signal X0(t) to be measured and the integrated signal X(t) have the same normalized waveform, so the pulse signal X0(t) to be measured and the integrated signal X(t) have the same leading edge time t r (unit is s) and signal length T (unit is s). In engineering practice, in order to reasonably configure the oscilloscope, it is required to pre-set the main parameters of the pulse signal X0 to be measured, such as amplitude U0, leading edge time t r The signal length T has been estimated, and the sensitivity K of the differential probe should be a known quantity.

[0076] Let the discrete signal obtained after the oscilloscope samples the differential monitoring signal x(t) be s(n), where n is the sequence number of the sampling point and the total number of sampling points is n. f , n f=T0 / t0. The DC and random components of the oscilloscope's noise floor are ε and η, respectively. The discrete signal s(n) is removed from the DC component ε, resulting in s1(n). Further removal of the random component η yields the discrete signal s2(n). Numerically integrating the discrete signals s(n), s1(n), and s2(n) yields the corresponding discrete integrated signals S(n), S1(n), and S2(n). Ideally, the discrete integrated signal S2(n) should match the integrated signal X(t) of the pulse being measured.

[0077] Define the oscilloscope sampling time interval as t0 and the vertical resolution as d0; the above physical quantities all adopt the MSK unit system.

[0078] The numerical integration method for autonomously eliminating zero-point drift of a pulse signal proposed in the present invention comprises the following steps:

[0079] Step 1. Set the oscilloscope sampling parameters, including sampling interval, sampling length, and vertical resolution;

[0080] The oscilloscope sampling time interval t0 must satisfy: t0≤t r / 20,t r is the leading edge time of the pulse signal X0(t) to be measured; that is, it is required that there are at least 20 sampling points within the leading edge time range of the pulse signal X0 to be measured. The oscilloscope sampling length T0 satisfies: T0 ≥ T, that is, the sampling period is greater than or equal to the length of the pulse signal X0(t) to be measured (that is, the time from the start of the pulse signal to the end of the pulse signal). The oscilloscope's vertical resolution d0 satisfies: d0 r ), where U / t r It is the average value of the amplitude change rate of the integral signal X(t) within the frontier time range, which is equivalent to the differential monitoring signal x(t) within the frontier time t r The average amplitude of the differential monitoring signal x(t) is required to be less than 1 / 30 of the average amplitude of the differential monitoring signal x(t) during the leading edge time.

[0081]

[0082] Step 2: Use an oscilloscope to sample the differential monitoring signal x(t) to obtain a discrete signal s(n). The discrete signal s(n) contains the discrete differential monitoring signal x(n) and the corresponding DC component ε(n) of the background noise and the random component η(n) of the background noise, that is:

[0083] s(n)=x(n)+ε(n)+η(n),n∈[1,n f ] (5)

[0084] ​x(n), ε(n), and η(n) are the discrete arrays corresponding to the differential monitoring signal x(t), the DC component ε of the background noise, and the random component η of the background noise after oscilloscope sampling; where n is the ordinal number of the sampling point, n f is the total number of sampling points, n f =T0 / t0,n f , n are both integers;

[0085] Step 3: Based on the sampling time interval t0, the discrete signal s(n) is numerically integrated to obtain the discrete integral signal S(n), that is:

[0086]

[0087] Step 4: Calculate the true value estimate ε0 of the DC component array ε(n) in the background noise;

[0088] Substituting formula (5) into formula (6) yields:

[0089]

[0090] According to the oscilloscope sampling time requirement in step 1, the discrete integral signal S(n) includes the time period before and after the integral signal X(t) of the pulse to be measured begins. Therefore, at the end point of the discrete integral signal S(n), the amplitude of the corresponding integral signal X(t) of the pulse to be measured is zero, that is:

[0091]

[0092] s(n) is the oscilloscope sampling signal, n f is the total number of sampling points, which also represents the signal length.

[0093] Substituting formula (8) into formula (7) yields:

[0094]

[0095] Since the expectation of the random component η of the background noise is 0, when the discrete integral signal S(n) is long enough, The value of is estimated to be 0, then (9) is simplified to:

[0096]

[0097] The statistical mean value ε0 of the DC component array ε(n) in the background noise is calculated according to formula (10), as shown in formula (11), where ε0 is an estimate of the true value of the array ε(n).

[0098] ε0=S(n f ) / (n f ·t0) (11)

[0099] Step 5: Assign values to the array ε(n).

[0100] In step 4, the true value estimate ε0 of the DC component ε in the background noise can be obtained according to equation (9). The DC component ε mainly comes from the thermal noise of the oscilloscope. When the temperature remains unchanged, the DC component ε should be a constant that does not change with time. The sampling length of the oscilloscope is generally less than 10μs. Within the μs time scale, the temperature of the oscilloscope device generally does not change. Therefore, the DC component ε can be regarded as a constant in theory. However, the value of the true value estimate ε0 of the DC component does not have an integer multiple relationship with the vertical resolution d0 of the oscilloscope, that is:

[0101]

[0102] In equation (12), h is the ratio of the estimated true value of the DC component ε0 to the vertical resolution d0 of the oscilloscope, rounded down. Since the discrete signal s(n) output by the oscilloscope can only be an integer multiple of the vertical resolution d0 of the oscilloscope, the sampling result ε(n) of the DC component in the background noise by the oscilloscope is a random array with a value of hd0 or (h+1)d0. The length of the array ε(n) is n. f , let n f The number of array elements with the value hd0 is n h , then n h The value of is:

[0103]

[0104] Then, in n f Randomly select n elements from the array h elements, assign them the value hd0, and assign the remaining array elements to (k+1)d0, and the assignment of the array ε(n) can be completed; the average value of the obtained ε(n) is ε0.

[0105] Step 6: Eliminate the influence of the DC component ε in the background noise of the discrete signal s(n) on the numerical integration, and obtain the discrete signal s1(n) after the DC component is eliminated.

[0106] s1(n)=s(n)-ε(n), n∈[1,n f ] (14)

[0107] Step 7: Further remove the influence of the random component η in the background noise of the discrete signal s1(n) on the numerical integration, and obtain the discrete signal s2(n) after the random component is eliminated.

[0108] According to step 6, the obtained discrete signal s1 is processed as follows for each element of the discrete signal s1: 1) the characteristic parameter k(n) in the discrete signal s1 is calculated,

[0109]

[0110] In formula (15), m is the characteristic parameter coefficient, which is adapted to the amplitude U of the integrated signal X(t). Referring to the requirements of step 1, the minimum value of m is 16. According to the constraints given in step 1: t0≤t r / 20,d0≤U / (30t r Substituting the above relationship into equation (13), we get the minimum value of m to be 16.

[0111] 2) If k(n) ≤ 1.3, set s1(n) to 0; if k(n) > 1.3, retain s1(n). This numerical processing eliminates the random component η from the discrete signal s1(n) and yields the random-component-eliminated discrete signal s2(n).

[0112] In step 7, the discrete signal s1(n) contains the differential monitoring signal x(n) and the random component η of the background noise, that is:

[0113] s1(n)=x(n)+η(n) (16)

[0114] The essence of step 7 is to determine whether the discrete signal s1(n) is correlated with the differential monitoring signal x(n). If the discrete signal s1(n) is not correlated with the differential monitoring signal x(n), that is, if s1(n) = η(n), the data in the discrete signal s1(n) is set to 0; otherwise, the data in the discrete signal s1(n) is retained.

[0115] To illustrate the effectiveness of step 7, we need to quantitatively explain the following two questions: First, the probability that the discrete signal s1(n) is set to 0 when s1(n) = η(n); Second, the probability that the discrete signal s1(n) retains data when s1(n) = x(n) + η(n). First, consider question 1:

[0116] Based on existing engineering experience, the oscilloscope background noise is statistically analyzed (the test method refers to the national military standard GJB 7691-2012). The standard deviation of the background noise obtained is generally slightly smaller than the vertical resolution d0 of the oscilloscope. Based on the above engineering experience, it can be assumed that η(n) obeys the expectation of 0 and the variance is d0 2 Normal distribution, that is, η(n)~N(0,d0 2 ).

[0117] When s1(n)=η(n), in formula (15) According to χ 2 Distribution definition, m·k(n) obeys χ 2 distribution, that is, m·k(n)~χ2 (m). Knowing that the minimum value of the m parameter is 16, find χ 2 The distribution table shows that when m ≥ 16, the probability of k(n) ≤ 1.3 is greater than 0.81, that is, P(k(n) ≤ 1.3 | m ≥ 16) > 0.81. In step 7, k(n) ≤ 1.3 is used as the threshold condition. If k(n) ≤ 1.3, the corresponding s1(n) is set to 0. Therefore, when s1(n) = η(n), processing the discrete signal s1 according to step 7 can eliminate 81% of the background noise η(n).

[0118] Let’s examine question 2 again. When s1(n) = x(n) + η(n), k(n) in equation (15) is:

[0119]

[0120] In the above formula, there are m x(n) involved in the accumulation operation. Let the minimum value of |x(n)| among the m x(n) be w·d0. Therefore, (17) can be derived as follows:

[0121]

[0122] Right now:

[0123] Define random variables A and B:

[0124]

[0125] Then formula (19) can be abbreviated as:

[0126]

[0127] Based on formula (20), we know that A ≥ 0; therefore, in formula (21), k(n) is negatively correlated with m. Furthermore, given that m ≥ 16, substituting this into formula (21) yields:

[0128] k(n)≥w 2 +2wB+0.0625A (22)

[0129] Given η(n)~N(0,d0 2 ), so η(n) / d0~N(0,1), substituting into formula (20) yields:

[0130]

[0131] Define the probability of A > A0 as P1 and the probability of B > B0 as P2. Given that η(n) / d0 follows a standard normal distribution, and based on the characteristics of the standard normal distribution, A and B are independent random variables; therefore, the probability of A > A0 and B > B0 is P1·P2. According to equation (21), the k(n) distribution is positively correlated with A and B, so:

[0132] k(n)≥w 2 +2Bw+0.0625A>w 2 +2B0w+0.0625A0 (24)

[0133] Formula (24) shows that: A>A0 and B>B0 is k(n)>w 2 +2B0w+0.0625A0 is a sufficient condition for this to hold. Therefore k(n)>w 2 The probability that +0.2B0w+0.1A0 holds true is P≥P1·P2, that is:

[0134] P(k(n)>w 2 +2B0w+0.0625A0)≥P1P2 (25)

[0135] Substituting m = 16 into formula (23), we can obtain by querying the probability distribution table that P1 = 1 when A > 0 and P2 = 0.996 when B > -0.675. Substituting into formula (25) we can obtain:

[0136] P(k(n)>w 2 -1.35w)>0.99 (26)

[0137] When w=2, w in formula (26) 2 -1.35w=1.3, substituting into (26) we can get

[0138] P(k(n)>1.3)>0.99 (27)

[0139] Since wd0 is the minimum value among the m |x(n)| values, |x(n)| ≥ 2d0. The above mathematical relationship expresses the following logic: when |x(n)| ≥ 2d0, the probability that k(n) > 1.3 is greater than 0.99. Referring to step 7, when k(n) > 1.3, the data s1(n) is retained. In other words, when |x(n)| ≥ 2d0, the probability P of retaining the data s1(n) is close to 1, P > 0.99.

[0140] Alternatively, when A>10, P1=0.87, and when 2B>-0.325, P1=0.75; substituting into formula (25), we obtain:

[0141] P(k(n)>w 2 -0.325w+0.625)≥0.65 (28)

[0142] When w=1, w in (28) 2 -0.325w+0.625=1.3, that is, P(k(n)>1.3)≥0.65. Therefore, when |x(n)|=d0, the probability that the data information of s1(n) is not set to 0 is greater than 0.65.

[0143] In summary, step 7 accurately determines whether s1(n) is correlated with x(n) and eliminates the noise floor η. When x(n) = 0, the probability of eliminating the noise floor η is greater than 80%. When |x(n)| is equivalent to the oscilloscope's vertical resolution d0, the probability of retaining x(n) is greater than 0.65. When |x(n)| ≥ 2d0, all waveform details of x(n) are preserved.

[0144] Step 8. Numerically integrate the discrete signal s2(n) over the sampling time interval t0 to obtain a discrete integrated signal S2(n). Compared with S(n), S2(n) eliminates the zero-point drift phenomenon caused by the oscilloscope background noise and can accurately reflect the waveform of the pulse X0(t) to be measured.

[0145]

[0146] For electrical pulse measurement systems based on differential probes, a numerical integration method is proposed to remove zero drift without manual intervention. This method effectively and autonomously eliminates the noise floor introduced by oscilloscope sampling, including its DC component ε and random component η, without distorting the monitoring signal measurement results.

[0147] Different from the existing method that takes the oscilloscope noise floor ε as a constant, this method defines the oscilloscope's sampling result of the noise floor ε(n) as a random array with the value hd0 or (h+1)d0, where h is the result of rounding down ε0 / d0, ε0 is the statistical average of ε(n), and d0 is the vertical resolution of the oscilloscope.

[0148] A strategy for eliminating the random component η is also proposed. This strategy retains the s1(n) data related to the oscilloscope monitoring signal x and sets the s1(n) data that does not contain the signal x and is only related to η to 0.

[0149] A criterion for accurately and efficiently judging whether each data in s1(n) is related to the monitoring signal x is also proposed. That is:

[0150]

[0151]

[0152] If k(n)≤1.3, then s1(n) is independent of x; if k(n)>1.3, then s1(n) is related to x.

[0153] Example: Take a differential measurement system installed on a flat transmission line as an example. Figure 2 As shown, the differential measurement system includes a differential probe and an oscilloscope, and the numerical integration method for autonomously eliminating the zero-point drift of the pulse signal provided by the present invention is introduced in detail.

[0154] A differential probe is used to sample the voltage pulse signal X0 between the high-voltage electrode and the ground electrode of the flat transmission line, and a differential monitoring signal x about X0 is output. The differential monitoring signal x is collected by an oscilloscope to obtain a discrete signal s, and the discrete signal s is numerically integrated to obtain a discrete integral signal S.

[0155] The estimated amplitude U0 of the measured voltage pulse X0 is 10 kV, and the leading edge time t r is 10 ns, and the signal length T is less than 400 ns. The sensitivity K of the differential probe is known to be 1.23×10 11 s.

[0156] As a reference, in Figure 1 A resistor divider is also used to measure the voltage pulse X0. The resistor divider outputs a measurement signal x0, which is sampled and recorded by an oscilloscope. Ideally, after normalization, the waveforms of the measurement signal x0 output by the resistor divider, the pulse signal to be measured X0, and the discrete integral signal S should be consistent. Therefore, the measurement signal x0 output by the resistor divider is used as a reference to evaluate whether the numerical integration method proposed in this invention can effectively eliminate the influence of the oscilloscope background noise on numerical integration. Figure 3 It is the waveform of the measurement signal x0 output by the resistor divider after normalization.

[0157] According to the numerical integration method for autonomously eliminating the zero drift of the pulse signal, the discrete signal s is numerically integrated. The processing steps are as follows:

[0158] Step 1) Complete the oscilloscope settings. The sensitivity of the differential probe is known to be K = 1.23 × 10 -11 s, the amplitude of the measured voltage pulse X0 is U0=10kV, the leading edge time is t r =10ns, signal length T>400ns; Substituting into (4) we get:

[0159]

[0160] Therefore, the oscilloscope configuration parameters are set as follows: sampling interval t0 = 0.4ns, sampling time length T0 = 1μs, and vertical resolution d0 = 0.4V.

[0161] Step 2) After completing the oscilloscope settings, use the oscilloscope to sample the differential monitoring signal x to obtain a discrete signal s, whose waveform is as follows Figure 4 shown.

[0162] Step 3) Based on the sampling time interval t0, the discrete signal s is numerically integrated according to formula (6) to obtain the discrete integral signal S, whose waveform is as follows Figure 5 As shown. Figure 5 and Figure 3 Compared with the waveform diagram of , it can be found that: affected by the background noise of the oscilloscope, the waveform of the discrete integral signal S after numerical integration has a significant zero drift phenomenon.

[0163] Step 4) Calculate the estimated value of the DC component ε in the background noise. From the known parameters, we know that the total number of data points n of the discrete signal s is f =T0 / t0=2500, the last data S(n f )=2.92×10 -7 According to equation (11), the estimated value of the true value of the DC component ε is ε0 = 0.292 V.

[0164] Step 5) Assign values to the array ε(n). Define the DC component ε in the oscilloscope background noise as an array with a length of n. f The random array ε(n) is hd0 or (h+1)d0. Given that ε0 = 0.292V, d0 = 0.4V, and h = 0 according to formula (12), the value of ε(n) is 0 or d0. f =2500, substituting into formula (13) to obtain n h =675. Using the Matlab library function randperm(n h , n f ), realize random selection of n in the array ε(n) h elements; the extracted n h The first element is assigned the value 0, and the remaining elements are assigned the value d0.

[0165] Step 6) According to formula (14), let s1(n) = s(n) - ε(n), eliminate the influence of the DC component ε in the background noise of the discrete signal s on the numerical integration, and obtain the discrete signal s1 after eliminating the DC component. Perform numerical integration on the discrete signal s1 to obtain the discrete integral signal S1, whose waveform is as follows Figure 6 As shown, Figure 5 Compared with the waveform of the original discrete integral signal S in the figure, the influence of the DC component ε in the background noise on the numerical integration is eliminated; however, compared with the Figure 3 Compared with the measurement signal x0 output by the resistor divider, the discrete integral signal S1 still has obvious low-frequency interference, which is caused by the background noise η.

[0166] Step 7) Further remove the influence of random component η in the background noise of discrete signal s1(n) on numerical integration. First, calculate the characteristic parameter coefficient m according to formula (15); from the known parameters: U0 = 10kV, K = 1.23×10 -11 s, d0 = 0.4V, t0 = 0.4ns, and we calculate m = 21. Substituting m = 21 into equation (15), we calculate the characteristic parameter k(n) of the discrete signal s1(n). Finally, we assign a value to s2(n) based on k(n): if k(n) > 1.3, s2(n) = s1(n); if k(n) ≤ 1.3, s2(n) = 0.

[0167] 8) Based on the sampling time interval t0, the discrete signal s2(n) is numerically integrated to obtain the discrete integral signal S2(n). According to formula (29), the calculation is completed to obtain the accurate numerical integral signal S2 of the pulse signal to be measured X0(t). The obtained discrete integral signal S2 waveform is normalized and compared with Figure 3 Compare the waveform of the measurement signal x0 output by the resistor divider in the figure, as shown in the figure below: Figure 7 and Figure 8 As shown, Figure 8 yes Figure 7 The comparison results show that the numerical integration method proposed in this invention effectively eliminates the influence of the oscilloscope background noise on the numerical integration results. When the oscilloscope input signal is 0, the waveform of the discrete integral signal S2 is a straight line tending to 0, which is consistent with the waveform of the measurement signal x0 output by the resistor divider. Figure 7 The above numerical integration method perfectly retains the waveform details of the measured voltage pulse X0. Figure 8 In the time period [-50ns, -150ns], the waveform of the discrete integral signal S2 is completely consistent with x0. The above experimental results show that the numerical integration method proposed in this invention can effectively eliminate the oscilloscope background noise without distorting the monitoring signal measurement results.

[0168] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present invention.

Claims

1. A numerical integration method for autonomously eliminating zero-point drift of a pulse signal, characterized in that: The following steps are involved: Step 1: Use a differential probe to measure the pulse signal X0(t) to obtain the differential monitoring signal x(t) of the pulse to be measured; Step 2: Set the oscilloscope sampling parameters, including sampling interval t0, sampling length T0, and vertical resolution d0; Step 3: Use an oscilloscope to sample the differential monitoring signal x(t) to obtain a discrete signal s(n). The discrete signal s(n) contains the discrete differential monitoring signal x(n) and the corresponding DC component ε(n) in the background noise and the random component η(n) in the background noise. s(n)=x(n)+ε(n)+η(n),n∈[1,n f ] Among them, n is the sequence number of the sampling point, n f is the total number of sampling points, n f =T0 / t0,n f , n are both integers; Step 4: Based on the sampling interval t0, the discrete signal s(n) is numerically integrated to obtain a discrete integral signal S(n); Step 5: Calculate the true value estimate ε0 of the DC component array ε(n) in the background noise; Step 6, assign values to the DC component array ε(n) so that the average value of the DC component array ε(n) is the true value estimate ε0; Step 7: Eliminate the influence of the DC component ε(n) in the background noise of the discrete signal s(n) on the numerical integration, and obtain the discrete signal s1(n) after the DC component is eliminated; s1(n)=s(n)-ε(n),n∈[1,n f ] Step 8: Eliminate the influence of the random component η in the background noise of the discrete signal s1(n) on the numerical integration, and obtain the discrete signal s2(n) after the random component is eliminated; Step 9: Perform numerical integration on the discrete signal s2(n) to obtain the integrated signal S2(n) after eliminating the zero drift:

2. The numerical integration method for autonomously eliminating zero-point drift of a pulse signal according to claim 1, characterized in that: Step 5 is as follows: 5.1, based on the last sampling moment X(n f ) has a zero amplitude and the expectation of the random component η is zero, and the discrete integral signal S(n f ): 5.

2. Calculate the true value estimate ε0 of the DC component array ε(n) in the background noise: ε0=S(n f ) / (n f ·t0)。 3. The numerical integration method for autonomously eliminating zero-point drift of a pulse signal according to claim 2, characterized in that: Step 6 is as follows: 6.

1. Determine the range of the true value estimate ε0 ε0∈[hd0,(h+1)d0], Wherein, h is the result of rounding down the ratio of the estimated true value of the DC component ε0 to the vertical resolution d0 of the oscilloscope; 6.

2. Calculate the number n of DC component arrays ε(n) with the value hd0 h : 6.

3. The array ε(n) has a total of n f elements, randomly select n of them h The first element is assigned the value hd0, and the remaining array elements are assigned the value (h+1)d0, so that the average value of the array ε(n) is the true value estimate ε0.

4. The numerical integration method for autonomously eliminating zero-point drift of a pulse signal according to any one of claims 1 to 3, characterized in that: In step 1, the time integral signal X(t) of the differential monitoring signal x(t) is: Define the amplitudes of the pulse signal X0(t) to be measured and the integrated signal X(t) to be U0 and U respectively; the leading edge time of the pulse signal X0(t) to be measured is t r ; The signal length of the pulse signal X0(t) to be measured is T; The sensitivity of the differential probe is K=U / U0; In step 2, the sampling interval t0 satisfies: t0≤t r / M; the sampling length T0 satisfies: T0≥T; the vertical resolution d0 satisfies: d0 r );​ Among them, M and P are sampling coefficient and quantization coefficient respectively.

5. The numerical integration method for autonomously eliminating zero-point drift of a pulse signal according to claim 4, characterized in that: Step 8 is as follows: 8.

1. Calculate the coefficient m of the characteristic parameter: 8.

2. Calculate the characteristic parameter k(n) of the discrete signal s1(n): 8.

3. Set the threshold Q and assign a value to the discrete signal s1(n) according to the characteristic parameter k(n): when k(n) ≤ Q, let s2(n) = 0; when k(n) > Q, let s2(n) = s1(n).

6. The numerical integration method for autonomously eliminating pulse signal zero drift according to claim 5, characterized in that: In step 8.1, m ≥ 16.

7. The numerical integration method for autonomously eliminating zero-point drift of a pulse signal according to claim 6, characterized in that: In step 8.3, Q = 1.

3.

8. The numerical integration method for autonomously eliminating zero-point drift of a pulse signal according to claim 7, characterized in that: In step 2, M≥20, P=30.

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