A method for designing a spectrum diagram of equipment vibration test by integrating spectrum energy and spectrum distribution

Abstract

The application discloses a kind of comprehensive spectrum energy and spectrum distribution equipment vibration test spectrogram design method, comprising: the acquisition signal of the subject equipment is segmented and intercepted according to different time length, and the Fourier transform of each segmented signal and acquisition signal after interception is carried out to obtain frequency spectrum signal;Whether there is sinusoidal vibration in frequency spectrum signal is identified by decibel conversion and sidelobe determination;If there is sinusoidal vibration, then extract sinusoidal signal from acquisition signal using Kalman filter, and determine the amplitude of sinusoidal signal;Subtract the sinusoidal signal in discrete form from acquisition signal to obtain residual signal;Power spectrum analysis is carried out to residual signal to obtain power spectral density, and the maximum envelope spectrogram of the power spectral density of multiple residual signals is solved;Flat section in maximum envelope spectrogram is identified using criterion, and standard spectrum is formulated;Finally, test spectrum is formed according to standard spectrum and the amplitude of sinusoidal signal.The present application provides guarantee for promoting the environmental adaptability performance bottom number evaluation of equipment.

Description

Technical Field

[0001] This invention belongs to the field of equipment environmental adaptability research, specifically involving a method for designing equipment vibration test spectrum based on integrated spectral energy and spectral distribution. Background Technology

[0002] Vibration, shock, and temperature are the main environmental factors that equipment experiences throughout its entire lifecycle, and they can damage the reliability of the equipment structure. Statistics show that environmental factors account for 52% of product failures, with vibration accounting for 27% of those failures. Vibration, through its full-frequency energy excitation, can induce multi-order resonances in the equipment structure, generating complex alternating stresses internally. This ultimately leads to material fatigue and the development of microcracks or even fractures. Simultaneously, it can cause fastener loosening, momentary electrical connection failures, solder joint detachment, and component damage, weakening mechanical integrity and leading to equipment performance degradation or functional interruption, posing a serious threat to reliability. Therefore, vibration tests are conducted during equipment development to assess the product's adaptability to environmental vibration.

[0003] Currently, equipment vibration environment testing methods are mainly based on the GJB150A-2009 standard, "Environmental Testing Methods for Military Equipment." However, given the significant differences between the vibration conditions in GJB150A-2009 and actual measurements in most equipment tests, it is impossible to accurately simulate the actual operating environment conditions of the test pieces. To more effectively assess the environmental vibration adaptability of products, using measured data to statistically summarize ground test conditions has become the mainstream trend in equipment development. Currently, domestic standards for vibration data summarization, such as HB / Z87-84 "Methods for Summarizing Aircraft Flight Vibration Environment Measurement Data" and GB / T10593.3-90 "Methods for Measuring Environmental Parameters of Electrical and Electronic Products, Vibration Data Processing and Summarization Methods," both employ the extreme value envelope method, statistically analyzing environmental data based on a certain confidence level and data percentile, without considering the data sample size and data distribution characteristics for unified processing. The statistical tolerance method proposed in GJB / Z126-2000, "Methods for Summarizing Measurement Data of Vibration and Shock Environments," determines an environmental envelope that covers the vast majority of individual observations within a given confidence level. It is worth noting that the methods provided by the above three standards ignore the energy distribution of the spectrum, making them generally more stringent. Furthermore, these methods sometimes equate sinusoidal signals to narrowband signals, which differs significantly from the actual operating environment of the product. Summary of the Invention

[0004] To address the issues of current vibration environment induction methods being subject to more stringent conditions and neglecting simple harmonic vibrations, the present invention aims to provide a method for designing equipment vibration test spectra that integrates spectral energy and spectral distribution. This method identifies sinusoidal and random vibrations in vibration signals and constructs equipment vibration test spectra based on measured data, according to the principle of energy equivalence.

[0005] To achieve the above objectives, the present invention employs the following technical solution: A method for designing vibration test spectra of equipment that integrates spectral energy and spectral distribution, comprising: The acquired signals from the tested equipment were segmented into segments of different time lengths. Fourier transforms were performed on each segment and the acquired signal to obtain the spectral signals. Decibels were converted and sidelobe analysis was used to identify the presence of sinusoidal vibrations in the spectral signals. If sinusoidal vibrations were found, Kalman filtering was used to extract the sinusoidal signal from the acquired signal, and the amplitude of the sinusoidal signal was determined. The discrete form of the sinusoidal signal was subtracted from the acquired signal to obtain the residual signal. Power spectral density was obtained by power spectral analysis of the residual signal, and the maximum envelope spectrum of the power spectral densities of multiple residual signals was calculated. Flat segments in the maximum envelope spectrum were identified, and a standard spectrum was established. Finally, the experimental spectrum was constructed based on the standard spectrum and the amplitude of the sinusoidal signal.

[0006] Furthermore, the presence of sinusoidal vibrations in the spectral signal is identified through decibel conversion and sidelobe determination, including: First, the spectrum signals corresponding to each segmented signal and the acquired signal are... Convert decibel values: ,in, This represents the converted decibel value; Indicates a reference value; Then, sinusoidal vibration is determined based on the converted decibel value: If the spectrum signal of the acquired signal is... There exists a frequency , making It is a local maximum, and the decibel value corresponding to this maximum is... and adjacent local minima The difference between the corresponding decibel values ​​is greater than or equal to the preset decibel threshold, and at the same time , , , , , If the sidelobe frequency deviation is within the preset frequency range, then the frequency is considered to be within the preset frequency range. A sinusoidal signal exists at that location; in, Represents the spectrum signal Zhongyu The frequencies corresponding to adjacent local minima; Represents the spectrum signal In frequency Spectral amplitude at that location; to These represent the frequency spectrum of each segment of the signal. The spectral amplitude at that location.

[0007] Furthermore, the Kalman filter is based on the following assumptions: ; in, Indicates the acquisition signal. Represents a discrete-time index. Indicates the total number of sampling points; Indicates the order of tracking; Indicates the harmonic order index; Indicates the first The first harmonic at time The amplitude; Indicates the estimated frequency In discrete time index The value; Indicates the sampling time interval; Indicates the acquired signal The error vector in.

[0008] Furthermore, let ,Will and As boundary conditions, the structure equations are as follows: ; in, to Indicates the first The first harmonic at time 1 to The amplitude; to Indicates the first The first harmonic at time 1 to Error term; Define the structure matrix ; Generalizing to a higher-order form, it can be represented as: ; in, Represents the acquired signal vector; This represents the state transition vector formed by concatenating state transition matrices of various orders; Represents the amplitude matrix; Represents the error vector; Minimizing using the least squares method, the partial derivative of the amplitude matrix is: ; in, Indicates the weighting coefficient; superscript Indicates the transpose operation; the superscript * indicates the conjugate symbol; This represents the residual under the constraint of amplitude smoothness. Represents the error vector; Represents the structure matrix; Therefore, amplitude matrix It can be represented as: ; in, Represents the identity matrix.

[0009] Furthermore, the amplitude matrix is ​​obtained by solving the least squares method. Then, the amplitude of each harmonic component at each time step can be obtained. This allows for the reconstruction of a complete sinusoidal signal. Discrete sampling is performed to obtain its discrete form. .

[0010] Furthermore, power spectral density is obtained by performing power spectral analysis on the residual signal, including: residual signal The signal is divided into multiple time segments, and a Discrete Fourier Transform is performed on each time segment to obtain the frequency domain data of each segment. Then the power spectral density is calculated. .

[0011] Furthermore, identifying the flat segments in the maximum envelope spectrum includes: Solve The average amplitude of the power spectral density of the group of acquired signals at the first spectral line and variance ;in This indicates the frequency corresponding to the first spectral line; The frequency corresponding to the first spectral line As a starting reference, the amplitude of the second spectral line adjacent to its frequency is compared with the range of values ​​determined by the first spectral line. Comparison: If the amplitude of an adjacent spectral line is the first spectral line If the values ​​are within the same range, they can be considered to be the same quantity, that is, belonging to the same straight segment; and so on, when the first... Root spectral line amplitude not When within the range, then the first The amplitude of the root spectral line is related to Compare; if it is within its range, then the first... The value of the first The roots are the same, belonging to the same straight segment; among them, Indicates the spectral line number; , Indicates the first The mean and variance of the amplitude at the root spectral line.

[0012] Furthermore, an experimental spectrum is constructed based on the standard spectrum and the sinusoidal signal, including: Based on the actual output capability of the test equipment used to apply the vibration environment, the straight segments of the standard spectrum are smoothly connected by oblique line segments; if a sinusoidal signal is identified in the acquired signal, the amplitude of the sinusoidal signal is superimposed on the test spectrum to form the final test spectrum.

[0013] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements a method for designing the equipment vibration test spectrum of the integrated spectral energy and spectral distribution.

[0014] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements a method for designing equipment vibration test spectra based on the integrated spectral energy and spectral distribution.

[0015] Compared with the prior art, the present invention has the following technical features: This invention comprehensively considers the characteristics of measured signals from equipment and proposes a standard spectrum design method for measured signals applicable to random signals, random plus narrowband signals, and random plus sinusoidal signals. It overcomes the problem of traditional extreme value envelope methods and parameter induction methods failing to identify sinusoidal signals in measured signals, achieving accurate estimation of measured signals and providing a guarantee for promoting the baseline assessment of equipment environmental adaptability performance. The experimental spectrum design method proposed in this invention is not only applicable to random signals but also to deterministic signals plus random signals, meeting the needs of experimental spectrum design for currently in-service equipment. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a partial view of the measured vibration signal of a certain piece of equipment in the embodiment; Figure 3 These are vibration signal spectra extracted at different time lengths in the embodiment; Figure 4 The following are vibration signal spectrum diagrams taken at different time lengths in the embodiment; Figure 5 The following are the vibration signal spectrum diagrams (amplitude values ​​in decibels) extracted at different time lengths in the embodiment. Figure 6 The following are low-frequency images of vibration signals (amplitude values ​​in decibels) taken at different time lengths in the embodiment. Figure 7 This is a time-domain waveform diagram of the Kalman filter at 21Hz in the embodiment; Figure 8 The Kalman filter spectrum at 21Hz is shown in the embodiment. Figure 9This is a time-domain waveform diagram of the residual signal in the embodiment; Figure 10 The power spectra of the five residual signals in the example are shown. Figure 11 This is the maximum envelope graph in the embodiment; Figure 12 The standard spectrum in the embodiment; Figure 13 The experimental spectrum is shown in the examples. Detailed Implementation

[0017] This invention discloses a method for designing vibration test spectra of equipment based on integrated spectral energy and spectral distribution. Addressing the problem of inductive spectrum design from measured data across the entire lifecycle of equipment, it considers both the randomness and determinism of equipment vibration signals. By comparing spectral differences at different time scales, a deterministic signal extraction method based on Kalman filtering is constructed to remove sinusoidal signals from the test signal. Then, combining the spectral characteristics of random signals, based on... The criteria determine the norm spectrum in random signals; based on this, a norm spectrum design applicable to equipment measured data is formed, providing support for equipment environmental adaptability assessment.

[0018] See Figure 1 The overall processing flow of the method of the present invention is as follows: the collected signals for the test equipment are processed... The signal is segmented into segments of different time lengths, and Fourier transforms are performed on each segment and the acquired signal to obtain the spectrum signal. The presence of sinusoidal vibrations in the spectrum signal is identified through decibel conversion and sidelobe detection. If sinusoidal vibrations are present, Kalman filtering is applied to the acquired signal. Extracting sine signals And determine the amplitude of the sinusoidal signal; from the acquired signal Subtract the discrete form of the sinusoidal signal from the middle Obtain the residual signal For residual signals Power spectral density is obtained by performing power spectral analysis, and the maximum envelope spectrum of the power spectral density of multiple residual signals is solved. ;use Criteria for identifying the maximum envelope spectrum In the straight segments, a standard spectrum is formulated; finally, based on the standard spectrum and the sinusoidal signal... This method constructs the experimental spectrum. It is applicable to the design of standard spectra for measured signals with random signals, random narrowband signals, and random sinusoidal signals. It overcomes the problem that traditional methods cannot identify sinusoidal signals in measured signals, and achieves accurate estimation of measured signals, thus providing a guarantee for promoting the baseline assessment of equipment environmental adaptability performance.

[0019] The present invention will be further described in detail below with reference to specific steps and embodiments.

[0020] Step 1: Segmented processing of acquired signals.

[0021] This step acquires the collected signals actually measured from the tested equipment, and segments them according to different time lengths to obtain multiple sets of signals at different time scales, providing a basis for subsequent multi-scale spectral comparison and analysis.

[0022] Specifically, the original vibration response signal (such as acceleration signal) actually measured from the tested equipment is acquired and recorded as the acquired signal. The collected signal The signal is segmented with time lengths of 0.5s, 1s, 2s, 5s, and 10s, and the segmented signals are denoted as follows: , , , , ;in, This represents a discrete-time index.

[0023] Step 2, Fourier transform.

[0024] This step performs Fourier transforms on the original acquired signal and each segment signal obtained in step 1 to obtain the corresponding spectral signals, providing a frequency domain basis for subsequent sinusoidal vibration identification.

[0025] Specifically, the acquired signal and segmented signal obtained in step 1 (in , Corresponding to the acquired signal, to Perform Fourier transforms on each segment of the signal to obtain the corresponding spectral signal. ;in Indicates frequency.

[0026] The expression for the Discrete Fourier Transform is: ; in, Represents a spectrum signal; This represents the length of the discrete signal, i.e., the total number of sampling points; Indicates the index of discrete sampling points in the time domain; Indicates the index of discrete points in the frequency domain; The imaginary unit that represents complex numbers; Represents the natural constant.

[0027] Step 3, sinusoidal vibration identification.

[0028] This step analyzes the spectral signals obtained in step 2, identifying the presence of sinusoidal vibrations in the acquired signals through decibel conversion and sidelobe detection. The frequency of the sinusoidal signal identified in this step will be used as the pre-estimated frequency for Kalman filtering in step 4.

[0029] Specifically, identify the spectral signal in step 2. To determine whether sinusoidal vibration exists, first convert the spectral amplitude obtained in step 2 into decibel values; the amplitude conversion formula is: ; in, This represents the converted decibel value; This represents a reference value; the signal collected in this scheme is an acceleration signal, therefore the reference value is... Usually chosen ; It represents the acceleration due to gravity.

[0030] Then, sinusoidal vibration is determined based on the converted decibel value: If the spectrum signal of the acquired signal is... There exists a frequency , making It is a local maximum, and the decibel value corresponding to this maximum is... and adjacent local minima The difference between the corresponding decibel values ​​is greater than or equal to 3dB, and at the same time , , , , , The sidelobe frequency deviation is in If it is within the range, then the frequency is considered to be within the range. A sinusoidal signal exists at that location.

[0031] in, Represents the spectrum signal Zhongyu The frequencies corresponding to adjacent local minima; Represents the spectrum signal In frequency Spectral amplitude at that location; to These represent the frequency spectrum of each segment of the signal. The spectral amplitude at that location.

[0032] Step 4, extract the sine wave signal.

[0033] This step uses Kalman filtering to extract the sinusoidal signal identified in step 3 from the acquired signal in step 1, thus separating the deterministic sinusoidal signal from the original acquired signal.

[0034] Specifically, based on the frequency of the sinusoidal signal identified in step 3 At this frequency As the pre-estimated frequency for Kalman filtering, a 1-second acquisition signal is extracted using Kalman filtering. sinusoidal signal ,in Indicates the extracted first A sinusoidal signal, This represents a continuous-time variable.

[0035] The Kalman filter algorithm is based on the following assumptions: ; in, Indicates the acquisition signal, This represents a discrete-time index, with values ​​ranging from 0 to... , Indicates the total number of sampling points; Indicates the order of tracking; Indicates the harmonic order index; Indicates the first The first harmonic at time The amplitude; Indicates the estimated frequency In discrete time index The value; Indicates the sampling time interval; Indicates the acquisition signal The signal components other than the currently estimated sinusoidal signal are treated as error vectors (estimation errors) of other spectral components during the filtering process.

[0036] make ,Will and As a boundary condition, the remainder The unknown amplitude at each moment constitutes the following structural equation: ; In the matrix , , The numerical values ​​are the coefficients of the structural equations; to Indicates the first The first harmonic at time 1 to The amplitude; to Indicates the first The first harmonic at time 1 to Error term.

[0037] Define the structure matrix .

[0038] Generalizing to a higher-order form, it can be represented as: ; in, Represents the acquired signal vector; This represents the state transition vector formed by concatenating state transition matrices of various orders; Represents the amplitude matrix; This represents the error vector. Specifically: ; in, Indicates the first The state transition matrix of order is: matrix, ; Indicates the first The first harmonic at time The value of the cosine function.

[0039] ; in, Indicates the acquisition signal At time 1 to The value; Indicates time 1 to The error value.

[0040] Minimizing using the least squares method, the partial derivative of the amplitude matrix is: ; in, Indicates the sign of the partial derivative; Indicates the weighting coefficient; superscript Indicates the transpose operation; the superscript * indicates the conjugate symbol; This represents the residual of the amplitude smoothness constraint, i.e., the degree of violation of the smoothness constraint on the change of amplitude between adjacent time points; Represents the error vector; Represents the amplitude matrix Conjugate; Represents the structure matrix; Represents the state transition vector . conjugate.

[0041] Therefore, amplitude matrix It can be represented as: ; in, Represents the identity matrix; superscript This represents finding the inverse of a matrix.

[0042] The amplitude matrix is ​​obtained by solving the above least squares method. Then, the amplitude of each harmonic component at each time step can be obtained. This allows for the reconstruction of a complete sinusoidal signal. This enables the transfer of the sinusoidal signal identified in step 3 from the acquired signal. Extracted from.

[0043] For sinusoidal signals With the acquisition signal Discrete sampling is performed using the same sampling frequency to obtain its discrete form. This is used for further processing in subsequent steps.

[0044] Step 5: Extract the amplitude of the sine wave signal.

[0045] This step performs a discrete Fourier transform on the sinusoidal signals extracted in step 4 to obtain the amplitude of each extracted sinusoidal signal, providing data for the superposition of sinusoidal signals in step 10.

[0046] Specifically, the sinusoidal signal extracted in step 4 Perform Discrete Fourier Transform to extract the amplitude of the sinusoidal signal. ,in This indicates the corresponding sine wave signal number.

[0047] Step 6: Calculate the residual signal.

[0048] This step subtracts all the sinusoidal signals extracted in step 4 from the original acquired signal to obtain the residual signal, which is the random vibration component.

[0049] Specifically, the acquired signal in step 1 Subtract the sinusoidal signals extracted in step 4 The residual signal is obtained. The calculation formula is as follows: .

[0050] Step 7: Power spectrum analysis of residual signal.

[0051] This step involves processing the residual signal obtained in step 6. Power spectrum analysis is performed to obtain the power spectral density of the residual signal, which provides the basis for solving the maximum envelope spectrum in step 8.

[0052] Specifically, the residual signal obtained in step 6 Perform power spectrum analysis; convert the residual signal Divided into There are 10 time recording segments, and the duration of each time recording segment is 1000. , of which The segment signal is denoted as , This represents the index of the time record segment; a discrete Fourier transform is performed on each time record segment to obtain the index of the time record segment. Segment signal at frequency point Frequency domain data at the location ,in Let represent the frequency domain index; then the expression for the power spectral density is: ; in, Indicates the first Power spectral density estimation of segment signals; express The model.

[0053] Signals for each time segment When performing windowing, the Hanning window function is used, and the window length is selected as follows: The window overlap coefficient is ;in, Indicates the sampling frequency.

[0054] Step 8: Solve for the maximum envelope spectrum.

[0055] This step processes and analyzes the power spectrum of multiple measured signals using the methods in steps 4 to 6, and solves for the maximum envelope spectrum of the power spectrum of each signal and the mean and variance of each spectral line.

[0056] Specifically, it is set up The group of signals were actually measured from the test equipment, of which the first group... The group of acquired signals is denoted as , Indicates the index of the acquired signal. For discrete-time indexing; for each group of acquired signals The process is performed using steps 4 through 6 respectively, to obtain the... Power spectral density of the residual signal corresponding to the group of acquired signals Solve Maximum envelope spectrum of the power spectral density of the group sampled signal and each spectral line (power spectral density) At discrete frequency points The amplitude at a given point is called the spectral line, and the mean and variance are calculated using the following formulas: ; in, Indicates the frequency point index.

[0057] Step 9: Develop the standard spectrum.

[0058] This step uses Criterion identification step 8 yields the maximum envelope spectrum. In the straight sections, standard spectra are formulated.

[0059] Specifically, adopt Criteria for identifying the maximum envelope spectrum The straight section in the middle; solve The average amplitude of the power spectral density of the group of acquired signals at the first spectral line and variance ;in This indicates the frequency corresponding to the first spectral line.

[0060] The frequency corresponding to the first spectral line As a starting reference, the amplitude of the second spectral line adjacent to its frequency is compared with the range of values ​​determined by the first spectral line. Comparison: If the amplitude of an adjacent spectral line is the first spectral line If the values ​​are within the same range, they can be considered to be the same quantity, that is, belonging to the same straight segment; and so on, when the first... Root spectral line amplitude not When within the range, then the first The amplitude of the root spectral line is related to Compare; if it is within its range, then the first... The value of the first The roots are the same, belonging to the same straight segment; among them, Indicates the spectral line number. ; Indicates the first The mean amplitude at the root spectral line; Indicates the first The variance of the amplitude at the root spectral line; connecting the identified straight segments sequentially according to their corresponding frequency ranges yields a stepped, standard spectrum composed of several horizontal line segments.

[0061] Step 10: Construct the experimental spectrum.

[0062] After obtaining the standard spectrum in step 9, based on the actual output capability of the test equipment (such as a shaking table) used to apply the vibration environment, the straight segments of the standard spectrum are smoothly connected by oblique line segments to form the test spectrum; the test equipment is a device used to simulate the vibration environment in a laboratory. If the acquired signal is identified in step 3... If the spectrum contains a sinusoidal signal, the amplitude of the sinusoidal signal obtained in step 5 is superimposed on the frequency corresponding to the experimental spectrum to form the final experimental spectrum.

[0063] Example: The method of the present invention will be further described in detail below through a specific embodiment. The parts that are repeated with the aforementioned steps in this embodiment will not be repeated; only the parameter settings and operational details of the specific implementation are given. The overall process is as follows: Figure 1 As shown.

[0064] 1. Signal acquisition and segmented processing.

[0065] Raw acquisition signal See Figure 2 The signal was segmented into time intervals of 0.5s, 1s, 2s, 5s, and 10s, and the segmented signals were denoted as follows: , , , , The time-domain waveforms of each extracted signal are shown below. Figure 3 .

[0066] 2. Fourier Transform and Sine Recognition.

[0067] For signals , , , , Perform Fourier transforms on each signal to obtain the corresponding spectral signals. , , , , The signal spectrum is shown below. Figure 4 The amplitude was converted to decibels, and the resulting spectrum is shown in the image. Figure 5 and Figure 6 . Figure 5 The image shows the entire converted spectrum (amplitude in decibels). It can be observed that there are no frequencies with significant energy in the mid-to-high frequency components, while there are spectral lines with significant energy in the low frequency components. Figure 6 This is the converted low-frequency graph, which shows... , , , , There are prominent amplitude components around 0Hz and 21Hz. The 0Hz component is a mean shift, which can be eliminated by removing the mean. The amplitude at 21Hz is greater than 3dB compared to the adjacent minimum, and in all five spectra, the sidelobes of the energy-prominent 21Hz component are all... Within this range, the signal can be determined. There is a sinusoidal vibration of 21 Hz.

[0068] 3. Kalman filtering is used to extract sine signals.

[0069] Based on the identified sinusoidal signal frequency of 21Hz as the pre-estimated frequency, a Kalman filter is used to extract the acquired signal with a time length of 1s. The extracted 21Hz sine wave signal is from the mid-sine wave signal. The time-domain waveform is shown in the figure. Figure 7 The extracted sinusoidal signal Perform a discrete Fourier transform, and the results are shown below. Figure 8 A sinusoidal signal can be observed in the figure. The frequency is 21Hz and the amplitude is 1.277g.

[0070] 4. Calculate the residual signal and perform power spectrum analysis.

[0071] Collected signals Subtract the extracted sine signal The residual signal is obtained. Its time-domain waveform is shown in Figure 9 Power spectral density of the residual signal is obtained by performing power spectral analysis. A Hanning window is used as the window function, and the window length is selected as... The window overlap coefficient is .

[0072] 5. Maximum envelope spectrum and standard spectrum formulation.

[0073] Power spectrum analysis was performed on the five measured signals using steps 4 to 6. The power spectra of each signal are shown below. Figure 10 Solve for the maximum envelope spectrum of the power spectra of five signals. ,See Figure 11 .

[0074] use Criteria for identifying the maximum envelope spectrum The straight segments in the middle are used to obtain the canonical spectrum, see Figure 12 .

[0075] 6. Construct the experimental spectrum.

[0076] After obtaining the standard spectrum, the corresponding straight segment is selected to determine the oblique line based on the capabilities of the experimental equipment, thus serving as the experimental spectrum. Since a 21Hz sine wave was identified in the measured signal during step 3, the extracted sine wave (frequency 21Hz, amplitude 1.277g) is added to the standard spectrum to form the final experimental spectrum, as shown in the experimental spectrum diagram. Figure 13 As shown.

[0077] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for designing vibration test spectra of equipment that integrates spectral energy and spectral distribution, characterized in that, include: The acquired signals from the tested equipment were segmented into segments of different time lengths. Fourier transforms were performed on each segment and the acquired signal to obtain the spectral signals. Decibels were converted and sidelobe analysis was used to identify the presence of sinusoidal vibrations in the spectral signals. If sinusoidal vibrations were found, Kalman filtering was used to extract the sinusoidal signal from the acquired signal, and the amplitude of the sinusoidal signal was determined. The discrete form of the sinusoidal signal was subtracted from the acquired signal to obtain the residual signal. Power spectral density was obtained by power spectral analysis of the residual signal, and the maximum envelope spectrum of the power spectral densities of multiple residual signals was calculated. Flat segments in the maximum envelope spectrum were identified, and a standard spectrum was established. Finally, the experimental spectrum was constructed based on the standard spectrum and the amplitude of the sinusoidal signal.

2. The method for designing equipment vibration test spectra based on integrated spectral energy and spectral distribution according to claim 1, characterized in that, Identifying the presence of sinusoidal vibrations in a spectral signal through decibel conversion and sidelobe determination includes: First, the spectrum signals corresponding to each segmented signal and the acquired signal are... Convert decibel values: ,in, This represents the converted decibel value; Indicates a reference value; Then, sinusoidal vibration is determined based on the converted decibel value: If the spectrum signal of the acquired signal is... There exists a frequency , making It is a local maximum, and the decibel value corresponding to this maximum is... and adjacent local minima The difference between the corresponding decibel values ​​is greater than or equal to the preset decibel threshold, and at the same time , , , , , If the sidelobe frequency deviation is within the preset frequency range, then the frequency is considered to be within the preset frequency range. A sinusoidal signal exists at that location; in, Represents the spectrum signal Zhongyu The frequencies corresponding to adjacent local minima; Represents the spectrum signal In frequency Spectral amplitude at that location; to These represent the frequency spectrum of each segment of the signal. The spectral amplitude at that location.

3. The method for designing equipment vibration test spectra based on integrated spectral energy and spectral distribution according to claim 1, characterized in that, The Kalman filter is based on the following assumptions: ； in, Indicates the acquisition signal, Represents a discrete-time index. Indicates the total number of sampling points; Indicates the order of tracking; Indicates the harmonic order index; Indicates the first The first harmonic at time The amplitude; Indicates the estimated frequency In discrete time index The value; Indicates the sampling time interval; Indicates the acquisition signal The error vector in.

4. The method for designing equipment vibration test spectra based on integrated spectral energy and spectral distribution according to claim 3, characterized in that, make ,Will and As boundary conditions, the structure equations are as follows: ； in, to Indicates the first The first harmonic at time 1 to The amplitude; to Indicates the first The first harmonic at time 1 to Error term; Define the structure matrix ; Generalizing to a higher-order form, it can be represented as: ； in, Represents the acquired signal vector; This represents the state transition vector formed by concatenating state transition matrices of various orders; Represents the amplitude matrix; Represents the error vector; Minimizing using the least squares method, the partial derivative of the amplitude matrix is: ； in, Indicates the weighting coefficient; superscript Indicates the transpose operation; the superscript * indicates the conjugate symbol; This represents the residual under the constraint of amplitude smoothness. Represents the error vector; Represents the structure matrix; Therefore, amplitude matrix It can be represented as: ； in, Represents the identity matrix.

5. The method for designing equipment vibration test spectra based on integrated spectral energy and spectral distribution according to claim 4, characterized in that, The amplitude matrix is ​​obtained by solving the least squares method. Then, the amplitude of each harmonic component at each time step can be obtained. This allows for the reconstruction of a complete sinusoidal signal. ; Discrete sampling is performed to obtain its discrete form. .

6. The method for designing equipment vibration test spectra based on integrated spectral energy and spectral distribution according to claim 1, characterized in that, Power spectral density is obtained by performing power spectral analysis on the residual signal, including: residual signal The signal is divided into multiple time segments, and a Discrete Fourier Transform is performed on each time segment to obtain the frequency domain data of each segment. Then the power spectral density is calculated. .

7. The method for designing equipment vibration test spectra based on integrated spectral energy and spectral distribution according to claim 1, characterized in that, Identifying flat segments in the maximum envelope spectrum, including: Solve The average amplitude of the power spectral density of the group of acquired signals at the first spectral line and variance ;in This indicates the frequency corresponding to the first spectral line; The frequency corresponding to the first spectral line As a starting reference, the amplitude of the second spectral line adjacent to its frequency is compared with the range of values ​​determined by the first spectral line. Comparison: If the amplitude of an adjacent spectral line is the first spectral line If the values ​​are within the same range, they can be considered to be the same quantity, that is, belonging to the same straight segment; and so on, when the first... Root spectral line amplitude not When within the range, then the first The amplitude of the root spectral line is related to Compare; if it is within its range, then the first... The value of the first The roots are the same, belonging to the same straight segment; among them, Indicates the spectral line number; , Indicates the first The mean and variance of the amplitude at the root spectral line.

8. The method for designing equipment vibration test spectra based on integrated spectral energy and spectral distribution according to claim 1, characterized in that, The experimental spectrum is constructed based on the standard spectrum and the sinusoidal signal, including: Based on the actual output capability of the test equipment used to apply the vibration environment, the straight segments of the standard spectrum are smoothly connected by oblique line segments; if a sinusoidal signal is identified in the acquired signal, the amplitude of the sinusoidal signal is superimposed on the test spectrum to form the final test spectrum.

9. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, When the processor executes the computer program, it implements the equipment vibration test spectrum design method based on the integrated spectral energy and spectral distribution as described in any one of claims 1-8.

10. A computer-readable storage medium storing a computer program; characterized in that, When the computer program is executed by the processor, it implements the equipment vibration test spectrum design method based on the integrated spectral energy and spectral distribution as described in any one of claims 1-8.

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