Artillery vibration environment simulation method based on impact response spectrum

Abstract

The present application belongs to the field of ground test technology in aviation system technology, and particularly relates to a gun vibration environment simulation method based on impact response spectrum. The gun vibration environment simulation method aims to improve the accuracy of simulation of gun vibration impact environment of aviation components in ground test. First, the resonance effect of gun frequency is analyzed, the amplification coefficients of low frequency and high frequency parts are calculated, and the intermediate transition SRS is formulated accordingly. Then, the parameterization dictionary matrix of the shock waveform is constructed, and the single-shot gun vibration impact signal is synthesized through an optimization algorithm. Subsequently, the single-shot gun vibration impact signal is copied, shifted and combined to form a repeated impact signal, and a full-band random noise signal is generated through a filter bank to compensate for the repeated gun vibration impact curve, and finally a multi-shot gun vibration impact environment time-domain waveform signal meeting the target SRS curve is formed. The present application can effectively improve the simulation effect of gun vibration impact environment ground test and more accurately test the impact environment adaptability of airborne equipment.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of ground test technology in aviation system technology, and relates to a gun fire vibration environment simulation method based on a shock response spectrum, in particular to a method for effectively simulating a gun fire vibration environment based on a shock response spectrum in a ground laboratory. BACKGROUND

[0002] Gun fire shock refers to the transient, high frequency, repeated excitation experienced by materials and structures during the process of gun firing, such as the vibration generated by the gun firing on an airplane. The characteristics of such shock are relatively short duration, but if multiple shots are fired, the shock will occur repeatedly.

[0003] The main problem of gun fire shock environment is that it can damage the structural and functional integrity of airborne equipment. Common structural failures include changes in the friction characteristics of the connection parts, permanent mechanical deformation, accelerated material fatigue, and cracks in brittle materials such as optical materials. In terms of functionality, gun fire shock can cause temporary changes in the performance of equipment components during the shock moment, or permanent changes after the shock, affecting insulation resistance, magnetic and electrostatic field strength, and piezoelectric properties. Therefore, it is necessary to test the equipment under gun fire shock in a laboratory shaker, which helps to evaluate the endurance of the equipment in the actual gun fire shock environment.

[0004] When gun fire shock testing is performed in a laboratory, a shaker (such as an electrodynamic vibration table) is needed to provide time history signal data. According to the most widely used military standard MIL-STD-810H, the generation of gun fire shock signals mainly adopts the following three methods: (1) measured data reproduction, (2) SRS (Shock Response Spectrum) generation, and (3) random plus sine generation. Currently, gun fire shock signal synthesis techniques mainly adopt methods (1) and (3), i.e., through the simulation of statistical characteristics of measured data and the combination of random plus sine techniques.

[0005] In many cases, it is not possible to obtain gun fire shock measurement data for in-service aircraft, so it is not possible to synthesize experimental signals based on statistical characteristics. This situation can occur when designing a new aircraft model or installing equipment in a new location. In these cases, a random generation method can be used to generate gun fire shock signals, the most representative method being the random plus sine method. However, this method is not suitable for simulating gun fire shock environments. The sine superimposed random vibration method provides a consistent rise time by superimposing harmonic-related sine components into stationary random vibration, but this is much lower than the rise time in a real gun fire shock environment, and its duration is much longer than that in a real gun fire shock environment. Therefore, the random generation method is not reliable and is usually used as a last resort to generate gun fire shock signals.

[0006] When the measured gun shock signal is not available, the shock response spectrum (SRS) generation method should be considered first. Based on the predicted gun shock SRS, a gun shock signal that fits the SRS curve can be generated. Since SRS is the most widely used method for comparing the severity of shock, the generated shock signal is considered to have the same destructive power as the actual gun shock impact. The standard MIL-STD-810 provides the basic requirements for generating signals from SRS. However, as of now, no effective method for synthesizing gun shock signals from SRS has been found in the public academic database. SUMMARY

[0007] In view of the deficiencies of the prior art, the present application provides a gun shock vibration environment simulation method based on the shock response spectrum, to accurately simulate the vibration environment of aviation equipment during the gun strike process under laboratory conditions, so as to evaluate and ensure the reliability of its structure and function.

[0008] S1, according to the resonance effect and the target SRS spectrum, an intermediate transition SRS is formulated.

[0009] The gun shock signal can be synthesized according to the target SRS, which simplifies the SRS into a piecewise function: a linear rising part in the low frequency range (expressed in logarithmic scale), and a flat platform part in the high frequency range. The target SRS can be expressed as:

[0010]

[0011] wherein

[0012] k: slope;

[0013] f: frequency variable;

[0014] F I : starting frequency;

[0015] F K : inflection point frequency;

[0016] F C : cut-off frequency;

[0017] A I : acceleration amplitude at starting frequency F I

[0018] A K : acceleration amplitude at inflection point frequency F K

[0019] wherein the slope k is defined as:

[0020]

[0021] As​​Figure 1 The synthesis process of gun vibration shock includes the following three steps: (a) synthesis of single shock event signals, (b) replication and splicing of single shock signals to form multiple shock signals, (c) addition of stationary random vibration for SRS compensation. When splicing multiple shock signals, especially in the low frequency band, due to the time interval between repeated single shock signals, these repeated signals will form a resonance phenomenon at a certain frequency. The frequency of resonance is closely related to the firing rate of the weapon, so an intermediate SRS can be constructed for single gun vibration, which has a lower amplitude of acceleration, and the single gun vibration signal generated based on this intermediate transition SRS will have its synthesized SRS at the same level as the target SRS.

[0022] The intermediate transition SRS is calculated as follows:

[0023]

[0024] where L I and L k are the amplification coefficients (dB) of the low and high frequency parts, respectively, obtained by analyzing the resonance effect caused by the firing frequency.

[0025] The slope k' in the low frequency range is usually between 6-12 dB / oct. According to the low frequency slope calculation formula, the inflection point frequency of the intermediate SRS can be calculated by the following formula:

[0026]

[0027] In this way, the intermediate transition SRS can be represented as:

[0028]

[0029] S2, analyze the time domain characteristics of single gun vibration shock signals, and construct a shock waveform parameterization dictionary matrix;

[0030] Synthesize single gun vibration shock signals according to the intermediate transition SRS obtained in S1. As Figure 2 shown, the single gun vibration shock signal is discretely modeled in the form of matrix multiplication:

[0031] u=Ga (7)

[0032] where u∈R M is a single gun vibration shock signal containing M samples, a∈R N is an amplitude vector, and matrix G∈R M×N contains N column vectors g, i.e., matrix G

[0033] [g1 g2 g3... g N ] (8)

[0034] In order to better control the temporal characteristics of the cannon shock (especially the initial rise time and effective duration), each column vector g is generated from the shock waveform function,

[0035] g(t)=(e ωζ(τ-t) +ζ τω(ln t-ln τ )·sin(ωt))*δ φ (t) (9)

[0036] Where t is the time variable, δ is the Dirac delta function with a time delay φ, ω = 2πf is the center frequency in radians, ζ is the damping ratio, τ is the rise time (the time when the envelope peak occurs), and '*' is the convolution operation. Using the convolution property, the delayed Dirac delta function is used to shift the impulse waveform to any time position. Equation (9) is given in amplitude-normalized form, where the absolute maximum amplitude is always 1.

[0037] The matrix G has N columns, each controlled by four unknown parameters, so a total of 4N parameters need to be defined. Applying the parameter dictionary design technique of the sparse representation method, let γ be the parameter space of G, which can be discretized into a parameter matrix Γ∈γ, where:

[0038]

[0039] is a 4×N matrix, the discrete impulse waveform g i is obtained by using the parameter vector γ i The input of formula (9) is given in Table 1 to better define the parameter space. The limit of frequency f depends on the frequency resolution and sampling rate of the signal, and the damping ratio is constrained by the normal physical range. The parameters τ and φ have an important influence on the rise time of the synthetic impulse, so they are set to the target rise time τ spec , the parameters in the matrix Γ can be obtained by solving the objective function:

[0040]

[0041] Table 1 Boundary constraints of shock waveform parameters

[0042]

[0043] Note: f s is the sampling rate of the signal.

[0044] Using the solution Γ′ obtained from formula (11), the matrix G′ can be calculated according to formula (9). Then, the impulse waveform sequence g′ is i The valid duration is checked and the waveforms that meet the conditions are combined into a new matrix G:

[0045] G = {g′ i |T(g′i ) < T spec} (12)

[0046] where T spec is the target duration. The function T(·) calculates the effective duration of a signal, for example, by the method of moving root mean square (RMS) provided by MIL-STD-810H. By following the selection process in equation (12), the effective duration of each shock waveform in matrix G meets the specification requirement. Therefore, the synthesized shock signal not only meets the requirement of effective duration, but also achieves the expected initial rise time.

[0047] S3, construct the objective function of single shot shock, and synthesize the time-domain curve of single shot shock environment.

[0048] For the problem of synthesizing a single shot shock, the main goal is to meet the required SRS specification. However, in addition, since the shock is essentially an elastic vibration of the structure, the amplitudes in the positive and negative directions need to have symmetry, so the "net zero displacement" is also an inherent requirement of the synthesized shock. Therefore, given the signal model, the problem of synthesizing a single shot shock can be transformed into a bi-objective optimization problem:

[0049]

[0050] where l(·) is the objective function, which measures the error, and SRS(·) is the conventional SRS calculation function. In this bi-objective optimization, l1 is used to measure the error between the synthesized single shot shock signal and the intermediate transition SRS, and l2 is used to measure whether the synthesized single shot shock signal meets the requirement of net displacement change. These objective functions can be minimized simultaneously, similar to the single-objective optimization problem, by combining the objective functions and substituting equation (7), the bi-objective optimization problem can be converted to the following form:

[0051]

[0052] where α controls the weight of the 'net zero displacement change' objective function. Given matrix G, the amplitude vector α can be accurately and efficiently calculated by heuristic algorithms such as genetic algorithms, simulated annealing algorithms, or particle swarm optimization. Subsequently, the single shot shock signal u is calculated by equation (7).

[0053] S4, copy, shift, and combine the single shot shock signal to form a repeated shock signal.

[0054] Through S3, the single shot shock signal u is obtained, and then it is copied, shifted, and combined, expressed as:

[0055]

[0056] Where n is the number of multiple arrivals, and λ is the time interval between adjacent arrivals. Although the displacement variation of the single shot waveform is minimum, the displacement variation of the synthesized waveform will increase n times, which cannot be ignored. n The component controls the net displacement variation of the multiple arrivals by canceling the displacement of the pair of shots. The time-domain image after splicing is shown in Figure 3 .

[0057] S5, generate a full-band random noise signal through a filter bank, synthesize a low-frequency noise curve of repeated shot impact, compensate the low-frequency noise curve to the repeated shot impact curve, and finally form a multi-shot impact environment time-domain waveform signal meeting the target SRS curve.

[0058] The repeated impact signal obtained in S4 also needs to add stationary random vibration to splice the impact signal for low-frequency noise compensation. The generated white noise signal r(t) follows a normal distribution:

[0059]

[0060] Apply the 1 / 12 octave filter bank of F' I to F' K to the white noise r(t) to generate a series of band-pass filtered signals:

[0061] r i (t)=(r*h i )(t) (17)

[0062] f i+1 =f i ×2 1 / 12 F I <f i <F′ K (18)

[0063] Where h i (t) is the impulse response of the i-th band-pass filter, and the center frequency is f i .

[0064] Model the low-frequency noise w(t) as a linear combination of band-pass signals:

[0065] w(t)=∑b i ·r i (t) (19)

[0066] Where b i is the amplitude parameter of each band-pass filtered noise. w(t) represents the low-frequency stationary noise of the multi-shot impact signal.

[0067] The amplitude parameter b i of the band-pass filtered signal can be controlled through another optimization problem.:

[0068]

[0069] In formula (20), the noise signal is added to the spliced impact signal v(t) for compensating its SRS to ensure that the SRS specification is met. Similar to the single-impact generation problem in formula (14), this optimization problem can also be solved by a commonly used heuristic algorithm. The finally generated multi-impact signal s(t) is obtained by adding the low-frequency noise w(t) to the spliced impact signal v(t):

[0070] s(t) = v(t) + w(t) (21)

[0071] The synthesized signal meets the target impact response spectrum specification.

[0072] Advantages

[0073] The present application controls the synthesis of the SRS time domain, realizes the synthesis of the multi-shot gun vibration impact environment time domain waveform for a given SRS, and simultaneously controls the time characteristics such as the initial rise time, duration of single impact and repetition interval of multi-impact based on the impact waveform dictionary technology. This technology effectively improves the overall simulation effect of the gun vibration impact environment ground test and more accurately tests the impact environment adaptability of airborne equipment. BRIEF DESCRIPTION OF DRAWINGS

[0074] Figure 1 It is a schematic diagram of the gun vibration impact signal synthesis step.

[0075] Figure 2 It is an algorithm flowchart of single-impact signal synthesis.

[0076] Figure 3 It is a waveform graph after the single-shot gun vibration impact signal is copied, translated and combined.

[0077] Figure 4 It is a target impact response spectrum (SRS) and an intermediate transition SRS spectrum type graph.

[0078] Figure 5 It is an impact waveform tiling graph of single-impact signal synthesis, wherein g1 to g10 are respectively the first ten impact waveform graphs in the parameter dictionary G.

[0079] Figure 6 (a) is an acceleration time history graph of the single-shot gun vibration impact signal synthesis result; Figure 6 (b) is an impact response spectrum (SRS) graph of the single-shot gun vibration impact signal synthesis result.

[0080] Figure 7 (a) is an acceleration time history graph after the multi-gun vibration impact signal is synthesized.Figure 7 (b) is the shock response spectrum (SRS) plot of the synthesized low frequency noise.

[0081] Figure 8 (a) is the acceleration time history plot of the synthesized low frequency noise; Figure 8 (b) is the shock response spectrum (SRS) plot of the synthesized low frequency noise.

[0082] Figure 9 (a) is the acceleration time history plot of the synthesized low frequency noise; Figure 9 (b) is the shock response spectrum (SRS) plot of the synthesized low frequency noise. DETAILED DESCRIPTION

[0083] The present application is further illustrated by the following specific examples, which are exemplary and are intended to be explanatory and explanatory of the present application, and are not a limitation.

[0084] 1. Target SRS of the shock test

[0085] The target SRS in this application is derived from MIL-STD-810H. Based on this target SRS, the intermediate transition SRS is generated to synthesize the single shot shock signal. I and L K are set to -9dB and -1dB, respectively. This is chosen based on the estimation of the resonance effect on the SRS after the shock splicing. The slope of the intermediate transition SRS is set to 6.4dB / oct. After these parameters are determined, the knee frequency of the intermediate SRS is calculated using equation (5). Table 2 lists the parameters of the target SRS and its corresponding intermediate transition SRS, Figure 4 shows two SRS curves.

[0086] Table 2 Target SRS of MIL-STD-810H standard and the parameters of the intermediate transition SRS

[0087]

[0088] 2. Synthesis of the single shot shock signal

[0089] The parameter matrix of the shock waveform dictionary is constructed. The duration T spec , the initial rise time τ spec , the weight α and the total number of basis functions N are set to 15ms, 4ms, 0.1 and 40, respectively. Based on these parameters, the dictionary matrix G is calculated through equations (7)-(11). Figure 5 shows the plot of the first ten shock waveforms in the parameter dictionary G. These waveforms are mainly concentrated in the duration of 15ms, and the time delay and the initial rise time are both less than 4ms, thus ensuring that they are substantially coincident at 4ms.

[0090] The amplitude vector a is solved from equation (13) using the particle swarm optimization algorithm, and then the shock waveform is weighted and superimposed according to its amplitude to generate a single shock signal, as shown in Figure 6 (a) and 6(b). The peak acceleration of the time history signal is 202.3 m / s 2 , and the effective duration and initial time are about 15 ms and 4 ms, respectively, which meet the requirements in the dictionary design process. The synthesized single shock signal oscillates around the zero axis, meeting the requirement of net zero displacement change. The SRS of the synthesized shock signal is highly consistent with the intermediate SRS, with almost no difference, strictly meeting the tolerance range of ±3 dB in the entire frequency range.

[0091] 3. Synthesis of multi-shot gun shock signals

[0092] The synthesized single shock is replicated multiple times, and the specific number of shocks can be arbitrarily set. In this study, a gun shock signal containing 20 shots is used as an example. These shocks are spliced into a repeated signal, with a 15 ms interval between each shock. This time interval is equal to the duration of a single gun shock, so there is no overlap between adjacent shock signals. These parameter settings correspond to a machine gun with a firing rate of 4000 rounds per minute, such as the M61A1 machine gun installed on the F-16 fighter jet. The time history and corresponding SRS are shown in Figure 7 (a) and 7(b), respectively. Due to the resonance effect, the SRS of the spliced shock is amplified in the low frequency range. This amplification effect is particularly evident compared to the intermediate transition SRS. The maximum resonance occurs at about 33 Hz, with an amplification ratio exceeding 6. Subsequently, more resonances are observed at odd multiples of 33 Hz, but the amplification ratio gradually decreases. The maximum resonance frequency is half of the firing rate, i.e., 66 Hz. This difference is due to the opposite amplitudes of the two adjacent single shocks in equation (15). Therefore, a low-frequency resonance is formed between each pair of adjacent shocks. However, due to the design of the correct intermediate transition SRS, the SRS envelope of the spliced shock exactly meets the target SRS.

[0093] The low-frequency noise signal is generated to compensate for the spliced shock. The white noise signal is randomly generated and filtered through a twelve-octave filter bank. The filtered signals with different center frequencies are superimposed by weighted sum, and the weights are calculated by the particle swarm optimization algorithm. The time history of the synthesized low-frequency noise and its SRS are shown in Figure 8 (a) and 8(b), respectively. The amplitude of the low-frequency noise is about 100 m / s 2, which is about half of the maximum amplitude of the synthesized blast, ensures that the noise signal does not cover the blast, thus preserving the temporal signature. The SRS of the low-frequency noise meets the target SRS in the low-frequency range, but there is a large gap at certain frequencies (e.g., 31 Hz). After 150 Hz, the acceleration amplitude drops and levels off in the high-frequency range.

[0094] The final synthesized multiple blast is shown in Figure 9 (a), which is the sum of the low-frequency noise and the spliced blasts. The temporal signature of each individual blast is well preserved and clearly shown in the time history. Figure 9 (b), the SRS of the synthesized multiple blast is compared with the target SRS. The SRS of the synthesized blast falls within the ±3 dB bandwidth throughout the entire frequency range. There are some fluctuations in the low-to-high frequency transition, which are about the inflection frequency of the middle SRS. Specifically, the maximum SRS error is 2.2 dB at 32 Hz, and the overall average error is only 0.45 dB. Therefore, the synthesized multiple blast signal well meets the requirements of the blast test.

[0095] The above embodiments are exemplary, and the purpose is to illustrate the technical concept and characteristics of the present application, so that those skilled in the art can understand the content of the present application and implement it, and cannot limit the protection scope of the present application. Any equivalent changes or modifications made in accordance with the spirit and essence of the present application shall be covered within the protection scope of the present application.

Claims

1. A method for simulating a gun vibration environment based on an impact response spectrum, characterized in that: Comprising the following steps: Step S1, according to the resonance effect and the target SRS spectrum, the intermediate transition SRS is formulated; Step S2, based on the time domain characteristics of single shot blast impact signal, the impact waveform parameterization dictionary matrix is constructed; Step S3, the objective function of single shot blast impact is constructed, and the time domain curve of single shot blast impact environment is synthesized; Step S4, the single shot blast impact signal is copied, shifted and combined to form a repeated impact signal; Step S5, generate full-band random noise signal, synthesize low-frequency noise curve of repeated blast impact, compensate low-frequency noise curve to repeated blast impact curve, and finally form multi-shot blast impact environment time domain waveform signal meeting target SRS curve; In step S1, The target SRS is expressed as: Wherein, k: slope; f: current frequency point; F I : start frequency; F K : inflection point frequency; F C : end frequency; A I : start frequency F I response amplitude at the frequency A K : response amplitude at the transition frequency F K : response amplitude at the transition frequency F Wherein, the definition of slope k is: The calculation of intermediate transition SRS is as follows: where L I and L k are the amplification coefficients (dB) of the low and high frequency parts, respectively, obtained by analyzing the resonance effect of the firing frequency; The inflection point frequency of intermediate SRS is calculated by the following formula: In this way, the intermediate transition SRS is expressed as: In step S2, The single shot blast impact signal is discretely modeled in the form of matrix multiplication: u=Gav where u e R M is a single shot vibro-impact signal comprising M samples, a e R N is an amplitude vector, the matrix G e R M×N comprises N column vectors g, i.e. the matrix G [g1 g2 g3...g N ] Each column vector g is generated from the impact waveform function: g(t) = (e ωζ(τ-t)+ζτω(lnt-lnτ) ·sin(ωt))*δ φ (t) Where t is the time variable, δ is the Dirac delta function with time delay φ, ω=2πf is the center frequency in radians, ζ is the damping ratio, τ is the rise time, '*' is the convolution operation; Using the convolution characteristics, the time delay Dirac delta function is used to move the impact waveform to any time position; The matrix G has N columns, each column is controlled by four unknown parameters, a total of 4N parameters need to be defined; Using the parameter dictionary design technology of sparse representation method, let γ be the parameter space of G, which is discretized into parameter matrix Γ∈γ, wherein: The parameter matrix Γ is a 4 x N matrix, the discrete shock waveform g i By using the parameter vector γ i As input to the equation; the bounds of the frequency f depend on the frequency resolution of the signal and the sampling rate, the damping ratio is constrained to the normal physical range; where the parameters τ and φ are set to a target rise time τ spec The parameters in the matrix Γ are obtained by solving the objective function: Using the solution Γ' of the above equation, the matrix G' is calculated according to the calculation formula of g(t), the effective duration of the shock waveform column g' is checked, and the shock waveforms meeting the conditions are combined into a new matrix G: i ​ G = {g' | T(g') < T i | T(g' | T(g') < T i ) < T spec} where T spec is the target duration, and the function T(·) computes the effective duration of the signal; In step S3, The synthesis problem of single shot blast impact is converted into a double objective optimization problem: Wherein, l(·) is the objective function, which is used to measure the error; SRS(·) is the conventional SRS calculation function; In this double objective optimization, l1 is used to measure the error between the synthesized single impact signal and the intermediate transition SRS, and l2 is used to measure whether the synthesized single impact signal meets the requirement of net displacement change; Minimizing these objective functions at the same time, the double objective optimization problem is converted into the following form: Wherein, α controls the weight of the 'net zero displacement change' objective function; Given matrix G, the amplitude vector α is calculated by heuristic algorithm; The heuristic algorithm is selected from: genetic algorithm, simulated annealing algorithm, particle swarm optimization; In step S4, The single shot blast impact signal is copied, shifted and combined, and the expression is: Wherein, n is the number of blast, and λ is the time interval of adjacent blast; In step S5, Generate white noise signal following normal distribution: F I to F K A 1 / 12 octave filter bank applied to white noise r(t) produces a series of bandpass filtered signals: r i (t) = (r * h i )(t) f i+1 = f i × 2 1 / 12 F I < f i < F' K where h i (t) is the impulse response of the i-th band-pass filter with center frequency f i ; Model the low-frequency noise w(t) as a linear combination of bandpass signals: w(t) = ∑b i • r i (t) where b i is the amplitude parameter of each band-pass filtered noise, representing the low-frequency stationary noise of the multi-impact signal; Adjusting the amplitude parameter b of a bandpass filtered signal by an optimization problem i to control the noise signal: Where the noise signal is added to the series impact signal v(t) to compensate for its SRS; The final multi-impact signal s(t) is obtained by adding low-frequency noise w(t) to spliced impact signal v(t) to meet the target requirement of target SRS: s(t)=v(t)+w(t).

2. The shock response spectrum-based gun fire vibration environment simulation method according to claim 1, characterized by: Adjusting an amplitude parameter b of a bandpass filtered signal i The optimization problem of the b parameter is solved using a heuristic algorithm.

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