A numerical integration method of differential signals for pulse measurement

Abstract

The present invention relates to a differential signal numerical integration method for pulse measurement; the method solves the problem that the result of direct integration of differential signals is greatly affected by measurement noise; the method specifically comprises the following steps: 1. intercepting the differential signal f(k), k=1, 2, ... N, collected by the differential sensor to obtain the background noise f(m), m=1, 2, ... T, T<(T0 / Δt), where T0 is the triggering time and Δt is the sampling interval; 2. based on the background noise f(m), intercepting the differential signal f(k), k=1, 2, ... N, obtaining the background noise f(m), m=1, 2, ... T, T<(T0 / Δt), wherein T0 is the triggering time and Δt is the sampling interval; 3. (k) is corrected to obtain the corrected differential signal f0(k); Step 3: numerically integrate f0(k) to obtain the integral sequence F(k) corresponding to the differential signal f0(k); Step 4: detrend the sequence F(k) to obtain the sequence F0(k); Step 5: extract the sequence F0(m) from the sequence F0(k), where m=1, 2, ...T, and based on F0(m), correct F0(k) by the following formula to obtain the measured electromagnetic pulse signal E(k).

Description

Technical Field

[0001] The present invention relates to a differential signal numerical integration method for pulse measurement, and in particular to a method for recovering a measured pulse signal from data acquired by a differential sensor when measuring an electromagnetic pulse signal. Background Art

[0002] Differential sensors are widely used in electromagnetic pulse signal measurement. They offer advantages such as being passive and simple in structure. Their output is the differential of the measured pulse signal. Recovering the measured signal involves integrating the signal obtained by the differential sensor. Integration methods include hardware integration and software integration. Hardware integration uses an integration circuit, but this increases the complexity of the measurement system and limits its bandwidth. Software integration uses numerical integration. However, since the differential signal obtained by the differential sensor contains measurement noise, direct numerical integration can lead to cumulative errors, resulting in large errors or even unusable results. Summary of the Invention

[0003] The purpose of the present invention is to solve the technical problem that the results obtained by the direct numerical integration method are greatly affected by measurement noise, and to propose a differential signal numerical integration method for pulse measurement.

[0004] The design idea of the present invention is:

[0005] Based on the trapezoidal integration method and the characteristics of the pulse signal, the noise information before and after the pulse signal is used to pre-process, detrend and post-process the differential signal to reduce the influence of measurement noise and obtain a higher quality numerical integration signal.

[0006] In order to achieve the above concept, the technical solution adopted by the present invention is:

[0007] A differential signal numerical integration method for pulse measurement is characterized in that it includes the following steps:

[0008] Step 1: Intercept the differential signal f(k) collected by the differential sensor, k = 1, 2, ... N, and obtain the background noise f(m) of the differential signal, m = 1, 2, ... T, T < (T0 / Δt), where T0 is the trigger time, Δt is the sampling interval, k and m are sampling points, and N is a positive integer;

[0009] Step 2: Based on the background noise f(m), the differential signal f(k) is corrected to obtain the corrected differential signal f0(k);

[0010] Step 3: Numerically integrate the modified differential signal f0(k) to obtain the integral sequence F(k) corresponding to f0(k);

[0011] Step 4: Detrend the integral sequence F(k) to obtain the detrended sequence F0(k);

[0012] Step 5: Extract the sequence F0(m) from the detrended sequence F0(k), where m=1, 2, ...T, and based on F0(m), correct F0(k) using the following formula to obtain the measured electromagnetic pulse signal E(k);

[0013] E(k)=[F0(k)-C]Δt k=1,2…N

[0014] Where, C = mean[F0(m)] m = 1, 2…T, and mean[] represents the average.

[0015] Furthermore, in step 2, the modified differential signal f0(k) is obtained by the following formula:

[0016] f0(k)=f(k)-C0 k=1,2…N

[0017] Where, C0=mean[f(m)] m=1,2…T.

[0018] Furthermore, in step 3, the numerical integration method is trapezoidal integration.

[0019] Furthermore, according to the principle that the two ends of the sequence do not contain pulse signals, but the middle sequence contains pulse signals, the integral sequence F(k) in step 3 is divided into three short sequences. After linear fitting of the short sequences at the front and back ends, the fitting coefficients a and b are obtained, and the detrended F0(k) is calculated by the following formula:

[0020] F0(k)=F(k)-ak-b k=1,2...N.

[0021] The beneficial effects of the present invention are:

[0022] 1. The present invention provides a differential signal numerical integration method for pulse measurement, which can provide a new method for electromagnetic pulse measurement.

[0023] 2. Compared with the circuit integration method, the present invention has the advantages of low cost, high accuracy, and no impact on the bandwidth performance of the measurement system.

[0024] 3. The method proposed in the present invention is simple and efficient. The algorithm can be integrated into the back-end data acquisition program, and the numerical integration results can be given in real time based on the measurement results at the test site. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1In an embodiment of the present invention, it is the measurement waveform of the differential sensor; where the abscissa is time, with the unit of second, and the ordinate is the output signal of the D-dot sensor;

[0026] Figure 2 In an embodiment of the present invention, it is the result after numerical integration using the solution of the present invention. Where the abscissa is time, with the unit of second, and the ordinate is the waveform restored by the method of the present invention;

[0027] Figure 3 It is the differentiation of an ideal pulse and the waveform after superimposing random white noise and DC bias;

[0028] Figure 4 It is Figure 3 the original waveform of the ideal pulse and the result of numerical integration by the solution of the present invention;

[0029] Figure 5 The flow chart of the present invention. Specific implementation manners

[0030] The present invention will be described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0031] The present invention proposes a method for numerical integration of differential signals for pulse measurement. As Figure 5 shown, it includes the following steps:

[0032] Step 1: Intercept the differential signal f(k), k = 1, 2,... N collected by the differential sensor to obtain the background noise f(m) of the differential signal, m = 1, 2,... T, T < (T0 / Δt), where T0 is the trigger moment, Δt is the sampling interval, k and m are both sampling points, and N is a positive integer; the specific value of the positive integer T can be selected according to experience, and when m < T, the待测 waveform has not appeared, and f(m) is only the background noise;

[0033] The method for obtaining the differential signal collected by the differential sensor is: making the output signal of the differential sensor pass through an A / D conversion device, and the relevant parameters of the sensor and the A / D conversion device meet the test requirements. The differential signal should be long enough to retain sufficient noise information;

[0034] According to the principle that the measured signal before the arrival of the pulse signal is the background noise, intercept the differential signal before the arrival of the pulse signal to obtain the background noise f(m) of the differential sensor. Under the condition of meeting the requirements, T should be as large as possible;

[0035] Step 2: According to the principle that the measured signal before the arrival of the pulse signal is the background noise, correct the differential signal f(k) to obtain the corrected differential signal f0(k);

[0036] Specifically: f0(k) is obtained through the following formula:

[0037] f0(k)=f(k)-C0 k=1,2…N

[0038] Where, C0=mean[f(m)] m=1,2…T, where mean[] means averaging;

[0039] like Figure 1 The following is the measurement result of a D-dot sensor (a differential sensor) in a certain experiment, with a sampling interval of Δt = 8×10 -11 s, T0 is 4376, N = 10000, T is 0.95 × T0, take the lower bound, T = 4157, and calculate C0 = -0.0049;

[0040] Step 3: Perform numerical integration on f0(k) to obtain the sequence F(k) corresponding to the differential signal f0(k);

[0041] In this embodiment, the numerical integration method is trapezoidal integration;

[0042] Step 4: Detrend the sequence F(k) to obtain the sequence F0(k);

[0043] Specifically, the method for detrending F(k), k=1,2,…,N is:

[0044] According to the principle that the two ends of the sequence do not contain pulse signals, but the middle sequence contains pulse signals, the sequence F(k), k = 1, 2, ..., N is divided into three parts, each of which has a length of N1, N2, N3, forming three parts G1(n1), G2(n2), and G3(n3) respectively, where n1 = 1, 2 ... N1, n2 = 1, 2 ... N2, n3 = 1, 2 ... N3, N1 + N2 + N3 = N. Linear fitting is performed on the parts G1(n1) and G3(n3) that do not contain obvious pulse signals to obtain the fitting coefficients a and b. Then, the sequence F0(k), k = 1, 2, ... N is obtained by the following formula;

[0045] F0(k)=F(k)-ak-b k=1,2…N

[0046] In this embodiment, the sequence corresponding to the differential signal is evenly divided into three parts, namely, N1 = 2000, N2 = 6000, and N3 = 2000. The first and third parts of the sequence are used for fitting (least squares method), and the fitting coefficients obtained are a = -0.0051 and b = -0.3804;

[0047] Step 5: Extract sequence F0(m) from sequence F0(k), where m=1, 2, ...T, and based on F0(m), correct F0(k) using the following formula to obtain the electromagnetic pulse signal E(k) under test;

[0048] E(k)=[F0(k)-C]Δt k=1,2…N

[0049] Wherein, C=mean[F0(m)]m=1,2…T, mean[] represents averaging, and the measurement signal result obtained by numerical integration of the present invention is as follows: Figure 2 shown.

[0050] To further illustrate the effectiveness of the method, numerical simulation was used to verify it. The specific process is to generate an ideal pulse, differentiate the waveform, and then superimpose random white noise with a signal-to-noise ratio of 40dB and a DC bias. The differential waveform and the generated result with superimposed noise and DC bias are shown in the figure below. Figure 3 As shown in (due to the inclusion of random noise, the results of each simulation are slightly different). The original pulse and the pulse waveform restored by the numerical integration method proposed in this invention are shown in Figure 4 As shown, the two have good adaptability, which illustrates the reliability of the method of the present invention.

Claims

1. A differential signal numerical integration method for pulse measurement, characterized in that: The following steps are involved: Step 1: Intercept the differential signal f(k) collected by the differential sensor, k = 1, 2, ... N, and obtain the background noise f(m) of the differential signal, m = 1, 2, ... T, T < (T0 / Δt), where T0 is the trigger time, Δt is the sampling interval, k and m are sampling points, and N is a positive integer; Step 2: Based on the background noise f(m), the differential signal f(k) is corrected to obtain the corrected differential signal f0(k); Step 3: Numerically integrate the modified differential signal f0(k) to obtain the integral sequence F(k) corresponding to f0(k); Step 4: Detrend the integral sequence F(k) to obtain the detrended sequence F0(k); Step 5: Extract the sequence F0(m) from the detrended sequence F0(k), where m=1, 2, ...T, and based on F0(m), correct F0(k) using the following formula to obtain the measured electromagnetic pulse signal E(k); E(k)=[F0(k)-C]Δt k=1,2…N Where, C = mean[F0(m)] m = 1, 2…T, and mean[] represents the average.

2. A differential signal numerical integration method for pulse measurement according to claim 1, characterized in that: In step 2, the modified differential signal f0(k) is obtained by the following formula: f0(k)=f(k)-C0 k=1,2…N Where, C0=mean[f(m)] m=1,2…T.

3. The differential signal numerical integration method for pulse measurement according to claim 1 or 2, characterized in that: In step 3, the numerical integration method is trapezoidal integration.

4. A differential signal numerical integration method for pulse measurement according to claim 3, characterized in that: The step 4 is specifically as follows: According to the principle that the two ends of the sequence do not contain pulse signals, and the middle sequence contains pulse signals, the integral sequence F(k) in step 3 is divided into three short sequences. After linear fitting of the short sequences at the front and back ends, the fitting coefficients a and b are obtained, and the detrended F0(k) is calculated by the following formula: F0(k)=F(k)-ak-b k=1,2…N.

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