A method for accurately measuring the transient duration of aircraft AC voltage

Abstract

A method for accurately measuring the transient duration of AC voltage in aircraft belongs to the field of electromagnetic metrology. The method involves: segmenting the waveform envelope for each time period and performing curve fitting; using numerical calculation to determine the coordinates of the intersection points of the fitted curves of adjacent envelope segments; treating these intersection points as inflection points for each transient time period; and directly calculating the duration of the transient segment by using the difference in time axis coordinates between adjacent inflection points; summing the transient durations of each segment yields the total transient duration, thus achieving accurate measurement of the AC transient duration. This invention divides the envelope into five time periods: pre-stabilization, build-up, continuation, recovery, and re-stabilization. It directly measures the transient duration using the difference in time axis coordinates of the inflection points of each time period. Since the transient envelope produces significant errors at inflection points where the AC transient waveform is not smooth, this invention avoids inflection point data, minimizing the impact of large errors in the demodulation envelope at inflection points on the measurement results.

Description

Technical Field

[0001] This invention relates to a method for accurately measuring the transient duration of AC voltage in aircraft, belonging to the field of electromagnetic metrology technology. Background Technology

[0002] Currently, research on the transient characteristics of aircraft AC power supply mainly focuses on estimating and measuring transient amplitude and waveform. In contrast, research on the precise measurement of transient duration is less common. However, the essence of power supply transients is not merely abnormal amplitude changes, but also instantaneous energy surges. Therefore, describing transients solely based on signal amplitude is far from sufficient; a simultaneous description of amplitude and time is necessary to clearly explain the impact of transients. The most crucial aspect of accurately measuring the duration of AC transient signals is determining the start and end points of the transient change. Currently, there are few methods that can accurately achieve this, primarily including the oscilloscope cursor method, transient envelope demodulation statistical methods, and wavelet decomposition to find singularities. These studies are mainly concentrated in the industrial power sector, and reports of measurements of the duration of AC transients in aircraft power supply characteristics accurate to the millisecond level are extremely rare.

[0003] In practical applications, rather than purely research-oriented fields, oscilloscopes are used to record waveforms in most cases. The inflection points of transient changes are then manually identified, and the oscilloscope cursor is used to measure the time of these inflection points. Due to human subjectivity, the test results always tend to align with the tester's desired outcome, especially when the measurement results are close to design limits. Furthermore, the oscilloscope cursor has limited resolution; sometimes, even with the intention to align the cursor in a favorable direction, the cursor may be positioned too far or too far. In reality, the resolvability of inflection points is much worse due to overshoot, preshoot, and noise. The cursor can not be positioned uniquely, resulting in significant errors, especially when measuring millisecond-level intervals, where relative errors reaching or exceeding 20% ​​are common. This is unacceptable in certain situations (such as calibration of aircraft power supply characteristics). The transient envelope demodulation statistical method uses the demodulated envelope of the transient waveform as the basis for measuring transient time parameters. It often employs statistical methods, but its accuracy is also not high. The wavelet rule focuses on studying the variation of transient points, identifying the information that differs between the variability points and the steady-state points, and then distinguishing them. It attempts to locate the position of the transient point on the time axis. It has a good effect when the singularity is very obvious, but the measurement effect is not ideal when the transient is not obvious or under the influence of noise, with large errors, and sometimes even misjudgment.

[0004] The solution to this problem is to standardize the process and use scientific methods for calculation instead of relying on visual observation and subjective human judgment. Summary of the Invention

[0005] To address the aforementioned problems, the present invention aims to provide a precise method for measuring the duration of AC transients by combining demodulation envelopes of sampled data with piecewise curve fitting. This method directly measures the transient duration using the difference in time axis coordinates of inflection points in each time segment. The invention involves segmenting the waveform envelopes of each time segment and performing curve fitting. The coordinates of the intersection points of the fitted curves of adjacent envelope segments are then calculated numerically. These intersection points are considered as the inflection points of each transient time segment. The duration of that transient segment is directly calculated using the difference in time axis coordinates between adjacent inflection points. The durations of all transient segments are then summed to obtain the total duration of the entire transient, thus achieving precise measurement of the AC transient duration.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] This invention discloses a method for accurately measuring the transient duration of an aircraft's AC voltage, comprising the following steps:

[0008] Step 1: Divide the transient duration into its various time intervals as follows:

[0009] Time period ①: The voltage operates smoothly at a certain value within the steady-state voltage range, which is the pre-stabilization stage;

[0010] Time period ②: The voltage changes from a steady-state value to a certain transient value, which is the transient build-up stage;

[0011] Time period ③: The voltage lasts for a short time under a certain unsteady voltage, which is the transient voltage duration stage; the short time refers to a time of less than 10 seconds;

[0012] Time period ④: The transient voltage recovers to another steady-state voltage, which is the stabilization process stage;

[0013] Time period ⑤: Stable operation under another steady-state voltage, which is the final stage.

[0014] Step 2: Waveform Data Acquisition

[0015] Using a data acquisition system, set the sampling parameters and obtain the sampling data of the complete voltage transient waveform for each time period described in step one;

[0016] Step 3: Waveform Preprocessing

[0017] The data collected in step two is preprocessed to remove redundant steady-state waveform sampling data before and after the transient state, resulting in preprocessed waveform data.

[0018] Step 4: Demodulate the outer envelope of the transient waveform

[0019] The waveform data preprocessed in step three is demodulated and transformed to obtain the demodulated envelope curve data of the AC voltage waveform;

[0020] Step 5: Transient waveform pre-segmentation

[0021] The transient envelope line is plotted using the demodulated envelope curve data from step four. Based on the time period division method in step one, the envelope line is roughly divided into five time periods: pre-stabilization, establishment, continuation, recovery, and re-stabilization.

[0022] Step 6: Perform piecewise fitting on the envelope curve.

[0023] Select each data segment and perform curve fitting within that segment to obtain the fitted curve equation for each segment;

[0024] The fitted curve equation for the pre-steady-state section is: V = f1(t);

[0025] The fitted curve equation for the established segment is: V=f2(t);

[0026] The fitted curve equation for the sustained segment is: V = f3(t);

[0027] The curve equation for the steady-state segment is: V = f4(t);

[0028] The fitted curve equation for the stable segment is: V = f5(t);

[0029] Step 7: Solve the equations of the two adjacent envelope waveforms simultaneously using numerical analysis to obtain the coordinates of the intersection point of the two curves.

[0030] Step 7.1: Joint

[0031]

[0032] Given two curve equations, use a numerical solution method to find the coordinates (t1, V1) of the intersection point A of these two curves.

[0033] Step 7.2: Joint

[0034]

[0035] Given two curve equations, use a numerical solution method to find the coordinates (t2, V2) of the intersection point B of these two curves.

[0036] Step 7.3: Joint

[0037]

[0038] Given two curve equations, use a numerical solution method to find the coordinates (t3, V3) of the intersection point C of these two curves.

[0039] Step 7.4: Joint

[0040]

[0041] Given two curve equations, use a numerical solution method to find the coordinates (t4, V4) of the intersection point D of these two curves.

[0042] Step 8: Calculate the transient duration to achieve accurate measurement of the AC transient duration.

[0043] The intersection points A, B, C, and D obtained in step seven are the inflection points of the transient change. The time coordinate axes for each inflection point are t1, t2, t3, and t4, respectively. Therefore, the duration T of each transient segment... i for:

[0044] T i =t i+1 -t i (i = 1, 2, ..., 4) (1)

[0045] The total duration T of the transient Σ for:

[0046] T Σ =t4-t1 (2)

[0047] The duration T of the sustained segment D for:

[0048] T D =t3–t2 ​​(3)

[0049] The duration T of the stabilization phase F for:

[0050] T F =t4-t3 (4)

[0051] If we disregard the transient setup time, the total duration of the transient is expressed as T. Z :

[0052] T Z =T D +T F =t4-t2 (5)

[0053] Unless otherwise specified, the transient duration is represented by equation (5)T. Z express.

[0054] The envelope of the aircraft's AC transient signal is extracted using signal envelope extraction methods (typically Hilbert transform). Then, based on the specific shape of the envelope, it is roughly segmented to obtain a rough estimate of the time coordinate τ at the inflection points of each segment. The raw data used to determine the fitted curve for each segment of the envelope.

[0055] Using the segmented raw sampling data, curve fitting is performed on each segment of the transient signal (typically, the least squares method is used to fit a straight line to an approximately linear change segment) to obtain the curve equation for each segment.

[0056] The equations of the fitted curves of two adjacent segments are solved together using numerical calculation methods to obtain the coordinates of the intersection point of the two fitted curves.

[0057] The intersection of two fitted curves is used as the precise start or end point of the transient. The time axis coordinate of the intersection is used to calculate the duration of each segment of the transient, thereby achieving accurate measurement of the duration of the AC transient.

[0058] Beneficial effects:

[0059] 1. This invention discloses a method for accurately measuring the duration of transient AC voltage in aircraft. It involves segmenting the waveform envelope for each time period and performing curve fitting. The coordinates of the intersection points of the fitted curves between adjacent envelope segments are then calculated numerically. These intersection points are considered the inflection points of each transient time period. The duration of the transient segment is directly calculated using the difference in time axis coordinates between adjacent inflection points. The durations of all transient segments are then summed to obtain the total duration of the transient. By eliminating the subjective influence of human visual perception on inflection point location, this invention enables accurate measurement of the duration of AC transients in aircraft power supply systems, provided the segmentation of the transient waveform envelope matches the actual situation.

[0060] 2. The present invention discloses a method for accurately measuring the transient duration of aircraft AC voltage. The envelope is roughly divided into five time periods: pre-stabilization, build-up, duration, recovery, and re-stabilization. The transient duration is directly measured by the difference in the time axis coordinates of the inflection points of each time period. Since the transient envelope will produce a large error at the inflection point where the AC transient waveform is not smooth, the present invention can avoid data near the inflection point when curve fitting (i.e., data near the inflection point does not participate in curve fitting). The large error of the demodulation envelope at the inflection point has little impact on the measurement results.

[0061] 3. This invention discloses a method for accurately measuring the transient duration of aircraft AC voltage. It involves segmenting the waveform envelope for each time period and performing curve fitting. The coordinates of the intersection points of the fitted curves for adjacent envelope segments are then calculated numerically, and these intersection points are used as the inflection points for each transient time period. Since noise has a very small impact on the curve fitting results, its influence on the calculation of the curve intersection points is also very small; that is, noise will not affect the calculation results of the transient inflection points. This makes the method highly noise-resistant. If the measurement accuracy does not need to be below 1ms, errors caused by random noise in the signal can be disregarded.

[0062] 4. The present invention discloses a method for accurately measuring the transient duration of aircraft AC voltage. By increasing the signal-to-noise ratio of the measured transient signal, the accuracy of the measurement result can be further improved. When the signal-to-noise ratio of the measured transient signal is greater than 40dB, the measurement result can be accurate to less than 0.2ms, which can be used in applications such as metrological calibration where accuracy requirements are very high. Attached Figure Description

[0063] Figure 1 Here is a block diagram of the experimental system for Example 1;

[0064] Among them: 1—Measurement and control computer, 2—Aircraft AC power supply transient signal generation device, 3—High-speed data acquisition system or digital storage oscilloscope, to record the complete waveform of the aircraft AC power supply transient voltage signal.

[0065] Figure 2 The division of the transient process of AC power supply voltage to an aircraft into different stages;

[0066] Figure 3 The original transient waveform was measured.

[0067] Figure 4 Measured waveform Hilbert transform demodulation envelope;

[0068] Figure 5 Simulated waveform of test voltage;

[0069] Figure 6 Hilbert transform demodulation envelope of simulated waveforms;

[0070] Figure 7 Hilbert demodulated waveform with noise of 0.2 Vrms;

[0071] Figure 8 Hilbert demodulated waveform with noise of 1.0 Vrms;

[0072] Figure 9 Hilbert demodulated waveform with noise of 5.0 Vrms. Detailed Implementation

[0073] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0074] Example 1:

[0075] This example is used to calculate the duration of the normal AC overvoltage transient process of an aircraft as specified in GJB181A-2003 "Aircraft Power Supply Characteristics".

[0076] To demonstrate the practical effectiveness of the measurement method described in this invention, the method was used to test the transient output waveform of a 400Hz / 115V voltage under actual operating conditions.

[0077] The measured object was the transient signal output from a California Instruments (CI) 15003iX programmable three-phase AC power supply. This signal is a transient limit signal for normal aircraft power supply, designed according to MIL-STD-704E requirements, and is stored in the equipment for retrieval during testing. Theoretically, the parameter requirements of this signal are consistent with those of GJB181A-2003, and also consistent with the simulated waveform data in Example 2. The experimental system block diagram is shown below. Figure 1 .

[0078] like Figure 1 As shown in the figure, the specific implementation steps of the method for accurately measuring the transient duration of aircraft AC voltage disclosed in this embodiment are as follows:

[0079] Step 1: Divide the transient duration into different time intervals.

[0080] The transient process can be divided into the following stages, taking high voltage transient as an example ( Figure 2 ):

[0081] Time period ①: The voltage operates smoothly at a certain value within the steady-state voltage range (pre-stabilization stage, before point A);

[0082] Time period ②: Voltage changes from steady-state value to a certain transient value (transient build-up phase AB);

[0083] Time period ③: The voltage lasts for a short time under a certain unsteady voltage (transient voltage duration process BC);

[0084] Time period ④: The transient voltage recovers to another steady-state voltage (stabilization process CD);

[0085] Time period ⑤: Stable operation under another steady-state voltage (end stage, after point D).

[0086] In practical work, for the convenience of measurement and research, the above stages are generally set as follows:

[0087] Unless the power supply system is in startup, the steady-state voltage transitions to transient voltage by changing linearly at the fastest speed of the power supply system (a relatively steep rise or fall on a straight line), and then remains at the transient voltage for a very short time (typically from 10 milliseconds to several seconds). Figure 2The middle finger represents a straight line parallel to the time axis. Afterward, based on the characteristics of load changes, it recovers to a steady state (a relatively slow downward or upward straight line), and finally returns to a steady state. Therefore, only segments BC and CD actually have specific time parameter requirements; the transient duration only requires determining the time T of segments BC and CD. D and T F Unless otherwise specified, the time interval AB is not included in the transient time.

[0088] Step 2: Waveform Data Acquisition

[0089] Using a data acquisition system, set the sampling parameters and obtain the sampling data of the complete voltage transient waveform for each time period described in step one;

[0090] The waveforms were recorded by a sampling digital power analyzer at a sampling rate of 100 kSa / s during an aircraft power supply characteristic adaptability test (commonly known as a power characteristic test) for a certain airborne product. See the specific waveform below. Figure 3 .

[0091] Step 3: Waveform Preprocessing

[0092] The data acquired in step two is preprocessed to remove redundant steady-state waveform samples before and after the transient, resulting in a preprocessed waveform. The steady-state amplitude V of the waveform before the transient is measured using the waveform data analysis function of a power analyzer. W1 ( Figure 2 The effective value of the AC voltage before point A), the transient amplitude V during the transient duration. T (RMS value of AC voltage in segment BC), steady-state amplitude V after the transient ends W2 .

[0093] V W1 V T V W2 Generally, the signal is measured by hardware during signal acquisition, or it can be obtained by waveform data analysis.

[0094] The following test results were obtained:

[0095] V W1 =115.957V;

[0096] V T =181.469V;

[0097] V W2 =119.195V;

[0098] Step 4: Demodulate the outer envelope of the transient waveform

[0099] The waveform data preprocessed in step three is demodulated and transformed to obtain the demodulated envelope of the AC voltage waveform.

[0100] In fact, the Hilbert transform is used to extract the envelope of transient signals, and the algorithm is as follows:

[0101] The Hilbert transform is a commonly used algorithm for extracting the envelope of a signal. It can provide a 90° phase change without affecting the amplitude of the spectral components. In other words, performing a Hilbert transform on a signal is equivalent to performing a quadrature phase shift on the signal, making it an orthogonal pair with itself. [2] The Hilbert transform cleverly applies the sine and cosine relationships between the real and imaginary parts of an analytical expression to define the instantaneous frequency, instantaneous phase, and instantaneous amplitude at any given moment. This solves the problem of defining and calculating instantaneous parameters in complex signals, making it possible to extract instantaneous parameters from both short and complex signals.

[0102] The principle of the Hilbert transform is as follows:

[0103] The Hilbert transform of a real function f(t) is defined as:

[0104]

[0105] H represents the Hilbert transform.

[0106] Therefore, the Hilbert transform is equivalent to passing through an impulse response as Linear network.

[0107] For the signal u(t) = a(t)cosθ(t), if we introduce v(t) = a(t)sinθ(t) to combine them into a complex signal:

[0108] V T1 =S1·t1+D1z(t)=a(t)cosθ(t)+ja(t)sinθ(t)=a(t)e jθ(t) Thus, the instantaneous envelope a(t), phase θ(t), and angular frequency ω(t) can be expressed as follows:

[0109] Instantaneous envelope:

[0110]

[0111] Instantaneous phase:

[0112]

[0113] Instantaneous angular frequency:

[0114]

[0115] Therefore, finding the instantaneous parameters of a signal u(t) reduces to finding v(t), i.e., its conjugate signal. For a signal u(t) = a(t)cosθ(t), its conjugate signal v(t) is the orthogonal component of the real part u(t), that is:

[0116]

[0117] By performing a Hilbert transform on the signal u(t), if its conjugate orthogonal component v(t) can be obtained, and then the signal is analytically represented, the three characteristic parameters of the signal, namely instantaneous amplitude, instantaneous phase, and instantaneous frequency, can be easily obtained, thus realizing true instantaneous parameter extraction. This invention only uses the Hilbert transform to obtain the envelope of the transient signal, i.e., formula (7).

[0118] The demodulation results of obtaining the transient waveform envelope using Hilbert transform are shown below. Figure 4 .

[0119] Step 5: Transient waveform pre-segmentation

[0120] Based on the demodulated envelope curve data from step four, a transient envelope line is plotted. The envelope line is roughly divided into five time periods: pre-stabilization (before point A), establishment (segment AB), continuation (segment BC), stabilization (segment CD), and re-stabilization (after point D) (reference). Figure 2 );

[0121] Step Six: Perform piecewise fitting on the envelope curve

[0122] Curve fitting was performed on each segment of data to obtain the fitted curve equations for each segment (the pre-stabilized segment, the establishment segment, and the complex stabilized segment were fitted with straight lines using the least squares method to obtain three straight line equations; the remaining two segments were fitted with the appropriate curve fitting method with small fitting error based on the envelope and the actual situation to obtain two other curve equations).

[0123] from Figure 2 It can be seen that the envelope of the transient characteristic parameters of the aircraft's AC power supply, reflected on the time-voltage coordinate axis, consists of several broken line segments. Each broken line segment is a segment of a straight line. Let the equations of the straight lines containing each segment AB, BC, and CD be as follows:

[0124] V = S1·t + D1 (10)

[0125] V=S2·t+D2 (11)

[0126] V=S3·t+D3 (12)

[0127] Step 6.1 Calculate the transient variation using the least squares fitting method

[0128] The typical application conditions for the least squares fitting method are that the input is precisely known, the output is a sequence of measured values ​​with errors, and the mathematical model of the input-output transformation characteristics is known. The purpose is to estimate the parameters of this model. Usually, it can be confirmed through experience or other means that the output and input are approximately linearly related; otherwise, the results are poor. The application condition faced by this method is that the output and the mathematical model of the input-output transformation characteristics are known (i.e., approximately linearly related), but the input corresponding to the output cannot be precisely known. Therefore, an additional application condition is that "each sampling time of the output measurement sequence must be strictly known"; otherwise, the least squares method cannot be used. The measurement sequence used in this invention is an equally spaced sampling sequence, which simplifies the operation and calculation.

[0129] A digital storage oscilloscope (or a digital sampling power analyzer) is used as the waveform measurement device to measure the transient signal of the aircraft's normal power supply AC voltage output from the aircraft power supply characteristic calibration signal source, obtaining the equally spaced measurement sequence V of the waveform. i The sequence is preprocessed to include a complete AC voltage transient process, with the first measurement point marking the starting point of the transition from steady-state voltage to transient voltage. The acquired sequence is denoted as V. i (i = 1, 2, ..., m). Let the acquisition rate of the digital storage oscilloscope (or power analyzer) be υ, and the sampling interval be τ, corresponding to V... i The sampling time is t i = (i-1)τ.

[0130] A segment of measurement sequence Vi that exhibits linear variation (such as the aforementioned "build-up phase" or "recovery phase") is extracted from the acquisition sequence, and the corresponding acquisition time is t. i = (i-1)τ+Kτ (i = 1, 2, ..., m), where K represents the sequence to be cut off starting from i = K+1, i.e., V i =V K+i Therefore, this measurement sequence is considered to conform to a linear law, and its model law is denoted as:

[0131] V = S·t + D

[0132] The least squares estimate of the slope S of the voltage rise or fall is:

[0133]

[0134]

[0135] The least squares estimate of the intercept D between the straight line and the AC voltage is:

[0136]

[0137] For the line segments corresponding to formulas (10) and (12), the S and D values ​​of each line AB and CD are calculated using the above two formulas respectively, and the results are:

[0138] S1=41172.44(V / s), D1=-265.5101(V);

[0139] S3=-809.3371(V / s), D3=197.3955(V).

[0140] Step 6.2 Piecewise fitting curve equation

[0141] Step 6.2.1: Curve fitting of the pre-stabilized segment (before point A)

[0142] The fitted curve equation for the pre-stable section (before point A) is: V = f1(t).

[0143] for Figure 4 In this regard, f1(t) can be simplified to:

[0144] V = f1(t) = V W1 = 115.957V (15)

[0145] Step 6.2.2: Curve fitting of segment AB

[0146] The fitted curve equation for the established segment (segment AB) is: V = f2(t);

[0147] V=f2(t)=S1·t+D1=41172.44t-265.5101 (16)

[0148] Step 6.2.3: Curve fitting of the continuous segment (BC segment)

[0149] The fitted curve equation for the continuous segment (segment BC) is: V = f3(t);

[0150] analyze Figure 4 f3(t) simplifies to:

[0151] V = f3(t) = V T =181.469V (17)

[0152] It should be noted that in many cases, the straight line corresponding to formula (11) is not linearly related to the sampling time. In such cases, it is not advisable to use the least squares method to calculate S and D. Other methods can be used to find the transient V. T .

[0153] Step 6.2.4: Curve fitting of the stabilization segment (CD segment)

[0154] The fitted curve equation for the complex stable segment (CD segment) is: V = f4(t);

[0155] V=f4(t)=S3·t+D3=-809.3371t+197.3955 (18)

[0156] Step 6.2.5: Curve fitting of the stable segment (after point D)

[0157] The equation of the curve after point D is: V = f5(t). For Figure 2 In other words:

[0158] V = f5(t) = V W2 =119.195V (19)

[0159] Step 7: Solve for the coordinates of the intersection points

[0160] Numerical analysis is used to solve the simultaneous equations of two adjacent envelope waveform segments to obtain the coordinates of their intersection points. The time coordinates of the intersection points of these segments with the three representative voltage curves (pre-stabilized, sustained, and complex-stabilized) are then determined. Specifically:

[0161] Step 7.1: Solve for the coordinates of the first intersection point A

[0162] joint

[0163]

[0164] Given two curve equations, we use a numerical solution method to find the coordinates (t1, V1) of the intersection point A of these two curves, and obtain the following:

[0165] t1 = 9.265 ms, V1 = 115.975 V

[0166] Step 7.2: Solve for the coordinates of the second intersection point B.

[0167] joint

[0168]

[0169] Given two curve equations, use a numerical solution method to find the coordinates (t2, V2) of the intersection point B of these two curves.

[0170] t2 = 10.856 ms, V2 = 181.469 V

[0171] Step 7.3: Solve for the coordinates of the third intersection point C.

[0172] joint

[0173]

[0174] Given two curve equations, we use a numerical solution method to find the coordinates (t3, V3) of the intersection point C of these two curves, and obtain the following:

[0175] t3 = 19.678 ms, V3 = 181.469 V

[0176] Step 7.4: Solve for the coordinates of the 4th intersection point D

[0177] joint

[0178]

[0179] Given two curve equations, the coordinates (t4, V4) of the intersection point D of these two curves are solved numerically, yielding the following:

[0180] t4 = 96.623 ms, V4 = 119.195 V

[0181] Step 8: Calculate the transient duration

[0182] Step 8.1 Calculation of the duration of each transient segment

[0183] The transient duration is calculated using the difference between the time axis coordinates, based on the precise definition of transient duration.

[0184] The intersection points A, B, C, and D obtained in step seven are the inflection points of the transient change. The time coordinate axes for each inflection point are t1, t2, t3, and t4, respectively. Therefore, the duration T of each transient segment... i for:

[0185] T i =t i+1 -t i (i = 1, 2, ..., 4) (20)

[0186] The total duration T of the transient Σ for:

[0187] T Σ =t4-t1 (21)

[0188] The duration T of the sustained segment D for:

[0189] T D =t3-t2=19.678-10.865=8.813(ms) (22)

[0190] The duration T of the stabilization phase F for:

[0191] T F =t4-t3=96.623-19.678=76.945(ms) (23)

[0192] If we disregard the transient setup time, the total duration of the transient can be expressed as T. Z :

[0193] T Z =T D +T F =t4-t2=96.623-10.865=85.758(ms) (24)

[0194] Unless otherwise specified, the transient duration is represented by equation (5)T. Z express.

[0195] Step 8.2 Explanation of Measurement Results

[0196] In contrast, GJB181A-2003 requires the following: T D =10ms, T F =77ms, T Z =87ms.

[0197] T D The error is mainly caused by the time resolution of the output device (the time resolution of the 15003iX when outputting a 400Hz transient waveform is only 1.25ms, which is half a cycle of 400Hz. Multiple tests have also proven that this device frequently and indeterminately adds or subtracts about 1.2ms from the transient waveform in some part, especially for transient waveforms with a time of less than 25ms). Z The error comes directly from T. D If it weren't for the resolution issue, the results would be more consistent.

[0198] Example 2:

[0199] Simulation experiment of ideal transient waveform

[0200] The test waveform uses the voltage transient limit waveform under normal operation of the aircraft's AC power supply. Theoretically, the envelope of the effective value of the AC voltage transient should meet the requirements of GJB181A-2003 "Aircraft Power Supply Characteristics". Figure 3 As required, the envelope in this invention refers to... Figure 2 Segments BC and CD are not given separately. For ease of analysis, in Figure 2 Two waveform segments, pre-stabilization and build-up, were added before the envelope. The simulation waveforms are shown below. Figure 5 .

[0201] The increased pre-steady-state voltage amplitude (RMS) is 118V for 10ms; the build-up period is set to 2.5ms with linear variation; the data sampling rate is 100kSa / s.

[0202] Thus, the specific values ​​of the simulated waveform are obtained as follows:

[0203] Pre-stabilized voltage V W1 =118V, transient V T =180V, instantaneous steady voltage V W2 =118V; Pre-stabilization time T b =10ms, build time T r = 2.5ms, transient duration T d =10ms, stabilization time T f =77ms, time T after recovery stabilization e =88ms.

[0204] Perform the measurement following the same steps as in Example 1.

[0205] Demodulate the waveform using the Hilbert transform to obtain the modulation envelope (see...). Figure 6 The sampled data and its sampling signal Hs(t) are used. The middle 200 points of Hs(t), which represent 80% of the data of the established segment, namely Hs(1026:1225), are taken and least squares fitted to obtain S1 = 26200.98 (V / s) and D1 = -145.4406 (V).

[0206] Similarly, the middle part of Hs(t), which represents 80% of the stable segment data, namely Hs(3021:9180), a total of 6160 points, is taken for least squares fitting, and S3 = -805.1994 (V / s) and D3 = 198.1172 (V) are obtained.

[0207] The equations of each curve segment are as follows:

[0208] Pre-stabilization phase (before point A): V = 118

[0209] Construction section (AB section): V = 26200.98t - 145.4406

[0210] Continuous range (BC segment): 180V

[0211] Stabilization phase (CD phase): V = -805.1944 + 198.1172

[0212] The stable phase (after point D); V = 180

[0213] Following the method in Example 1, we solve for the coordinates of points A, B, C, and D by combining the above equations, and obtain (t1,V1), (t2,V2), (t3,V3), and (t4,V4).

[0214] Using equations (22), (23), and (24), we can obtain:

[0215] T D=0.010093(s) =10.093ms;

[0216] T F =0.076986(s) =76.986ms;

[0217] T Z =0.087079(s) =87.079ms.

[0218] The errors from the set values ​​were 0.093ms, -0.014ms, and 0.079ms, respectively.

[0219] It should be noted that there is no V here. W1 V W2 V T The set values ​​are used in the calculation, and these values ​​are obtained directly from the envelope through a simple average.

[0220] Simulation experiment of superimposed noise transient waveform

[0221] To more accurately reflect the actual situation, noise with effective values ​​of 0.2V, 1V, and 5V was superimposed on the original waveform for further testing. The demodulated envelope is shown below. Figure 7 , Figure 8 , Figure 9 The results are shown in Table 1.

[0222] Table 1 Comparison of simulation results under different noise levels

[0223]

[0224] The results show that the measurement method is insensitive to signal noise.

[0225] 1) For the AC transient signal of an aircraft, as long as there is a waveform with good linearity in the establishment and stabilization phases, and the linear change trend of this waveform can reflect the overall change trend of the waveform, this waveform data can be used to represent the data of the entire segment, participate in least squares fitting, and finally obtain the accurate measurement result of the duration of the AC transient signal.

[0226] 2) The Hilbert transform produces a large error at the inflection point of the AC transient waveform where it is not smooth. The method proposed in this invention avoids the inflection point data. The large error of the demodulation envelope of the Hilbert transform at the inflection point has little impact on the measurement results.

[0227] 3) This embodiment has very strong noise resistance. If the measurement results do not require accuracy to less than 1ms, the error caused by random noise in the signal can be ignored.

[0228] 4) In this embodiment, for signals with a signal-to-noise ratio greater than 40dB, the measurement results can be accurate to less than 0.2ms, which is suitable for applications with high accuracy requirements such as metrological calibration.

[0229] Example 3:

[0230] This embodiment discloses a method for accurately measuring the transient duration of aircraft AC voltage, and the specific implementation steps are as follows:

[0231] Step 1: Obtain the sampling data of the transient waveform;

[0232] Step 2: Determine the parameter settings for sampling;

[0233] Step 3: Preprocess the waveform to obtain the steady-state amplitude before the transient occurs, the transient amplitude during the transient duration, and the steady-state amplitude after the transient ends (generally measured by hardware during signal acquisition, or obtained by waveform data analysis measurement). Remove redundant steady-state waveform data before and after the transient.

[0234] Step 4: Perform Hilbert transform on the waveform data to obtain the demodulation envelope of the waveform;

[0235] Step 5: Draw the envelope and divide it into five time periods: pre-stabilization, establishment, continuation, recovery, and re-stabilization.

[0236] Step 6: Select the data that is relatively linear between the two segments of the establishment state and the stable state (without loss of generality, take about 10% to 90% of the data), and perform least squares fitting according to Equation (13) and Equation (14) to obtain the slopes S1 and S3 and the intercepts D1 and D3 of the two lines.

[0237] Step 7: Determine the time coordinates of the intersection points of the two lines mentioned above with the three lines representing the pre-stabilized, continuous, and re-stabilized voltages;

[0238] Step 8: Calculate the duration parameter from the difference in time coordinates to achieve accurate measurement of the duration of AC transients.

[0239] After obtaining the two sets of data, S1, S3 and intercepts D1, D3, you can also refer to the following steps to calculate the measurement results.

[0240] Without loss of generality, we can assume S1 > 0 to describe the rising edge of the transient voltage, and S3 < 0 to correspond to the falling edge of the transient voltage. Theoretically, the intersection of equation (10) and the pre-steady-state voltage is the starting point A of the voltage transient. Let's assume this time is t1, and its ordinate is the pre-steady-state voltage V1, that is:

[0241] V1=S1·t1+D1 (25)

[0242] Since V1 is generally known (V1 = VW1 (This can be measured using an AC voltmeter or other means), thus we can obtain:

[0243]

[0244] The intersection of equations (10) and (11) is the starting point of the AC voltage change from steady state to transient state. Let the time at this moment be t2, which is the starting point of the transient voltage duration. Its ordinate is the AC transient voltage V. T That is:

[0245] V T =S1·t2+D1 (27)

[0246] In most cases, AC transient voltage V T If the value does not change over time during the duration, i.e., S2 = 0 in equation (11), then equation (11) becomes: V = D2 = V T

[0247] V T Since V can be obtained through other methods, then... T Given that, from equation (10), we get:

[0248]

[0249] Therefore, the moment when the transient voltage begins is:

[0250] The transient voltage lasted for T D After a certain time, it reaches time point t3, then decays linearly according to equation (12) and returns to a certain stable voltage V2. The x-coordinate of the intersection of equations (11) and (12) is the end point t3 of the transient duration. From equation (12), we get

[0251] V T =S3·t3+D3 (29)

[0252] The moment when the transient voltage ends is:

[0253]

[0254] After the transient voltage duration ends, the process of recovering to another steady-state voltage begins. The voltage change curve at this time is represented by equation (12). When the voltage returns to a certain stable value, the transient process ends. The straight line represented by equation (12) intersects with the steady-state voltage V2 = V W2 The intersection of the straight lines is the end point of the entire transient process, which can be obtained from equation (12).

[0255] V2 = S3·t4 + D3, therefore we have

[0256]

[0257] AC voltage transient V T Duration T D for:

[0258]

[0259] The AC voltage changes from a transient state to another steady-state voltage V W2 The time (called transient recovery time) T F for:

[0260]

[0261] The total time of the entire voltage transient process is:

[0262]

[0263] Therefore, as long as we can find out the starting and ending voltages (V1, V2) of the transient voltage and find out the change law of the transient voltage, that is, find out S1, D1, S3, D3, we can find out the time parameters according to equations (32), (33), and (34).

[0264] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for accurately measuring the transient duration of an aircraft's AC voltage, characterized in that: Includes the following steps: Step 1: Divide the transient duration into its various time intervals as follows: Time period ①: The voltage operates smoothly at a certain value within the steady-state voltage range, which is the pre-stabilization stage; Time period ②: The voltage changes from a steady-state value to a certain transient value, which is the transient build-up stage; Time period ③: The voltage lasts for a short time under a certain unsteady voltage, which is the transient voltage duration stage; the short time refers to a time of less than 10 seconds; Time period ④: The transient voltage recovers to another steady-state voltage, which is the stabilization process stage; Time period ⑤: Stable operation under another steady-state voltage, marking the end of the process; Step 2: Using a data acquisition system, set the sampling parameters and obtain the sampling data of the complete voltage transient waveform for each time period described in Step 1; Step 3: Preprocess the data collected in Step 2 to remove redundant steady-state waveform sampling data before and after the transient state, and obtain the preprocessed waveform data. Step 4: Demodulate and transform the waveform data preprocessed in Step 3 to obtain the demodulated envelope curve data of the AC voltage waveform; Step 5: Plot the transient envelope line from the demodulated envelope curve data in Step 4. Based on the time period division method in Step 1, roughly divide the envelope line into five time periods: pre-stabilization, establishment, continuation, recovery, and re-stabilization. Step 6: Select each data segment and perform curve fitting within that segment to obtain the fitted curve equation for each segment; The fitted curve equation for the pre-steady-state section is: V = f1(t); The fitted curve equation for the established segment is: V=f2(t); The fitted curve equation for the sustained segment is: V = f3(t); The fitted curve equation for the stable phase is: V = f4(t); The fitted curve equation for the stable segment is: V = f5(t); Step 7: Solve the equations of the two adjacent envelope waveforms obtained in Step 6 using numerical analysis to obtain the coordinates of the intersection point of the two curves. Step 7.1: Joint Given two curve equations, use a numerical solution method to find the coordinates (t1, V1) of the intersection point A of the two curves. Step 7.2: Joint Given two curve equations, use a numerical solution method to find the coordinates (t2, V2) of the intersection point B of the two curves. Step 7.3: Joint Given two curve equations, use a numerical solution method to find the coordinates (t3, V3) of the intersection point C of these two curves. Step 7.4: Joint Given two curve equations, use a numerical solution method to find the coordinates (t4, V4) of the intersection point D of the two curves. Step 8: The intersection points A, B, C, and D obtained in Step 7 are the inflection points of the transient change; the time coordinate axes of each inflection point are t1, t2, t3, and t4, respectively. Then, the duration T of each transient segment is... i for: T i =t i+1 -t i ,(i=1,2,…,4) (1) The total duration T of the transient Σ for: T Σ =t4-t1 (2) The duration T of the sustained segment D for: T D =t3-t2 (3) The duration T of the stabilization phase F for: T F =t4-t3 (4) If we disregard the transient setup time, the total duration of the transient is expressed as T. Z : T Z =T D +T F =t4-t2 (5) The transient duration is expressed by equation (5)T Z express.

2. The method as described in claim 1, characterized in that: The envelope of the aircraft's AC transient signal is extracted using a signal envelope extraction method. Based on the specific shape of the envelope, it is roughly segmented to obtain a rough estimate of the time coordinate τ at the inflection point of each segment. The raw data used to determine the fitted curve for each segment of the envelope.

3. The method as described in claim 1, characterized in that: Using the segmented raw sampling data, curve fitting is performed on each segment of the transient signal to obtain the curve equation for each segment.

4. The method as described in claim 1, characterized in that: The equations of the fitted curves of two adjacent segments are solved together using numerical calculation methods to obtain the coordinates of the intersection point of the two fitted curves.

5. The method as described in claim 1, characterized in that: The intersection of the two fitted curves is used as the precise start or end point of the transient, and the time axis coordinates of the intersection are used to calculate the duration of each segment of the transient.

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