A micro-vibration superposition response frequency division prediction method and system for a multi-vibration source environment of a precision instrument, and a storage medium

Abstract

This invention discloses a frequency division prediction method, system, and storage medium for micro-vibration superposition response in multi-source environments for precision instruments. The method obtains the structural vibration response of the target response point under the action of each single vibration source, determines the corresponding response power spectral density, and constructs a total response power spectral density expression including self-spectral and cross-spectral terms under linear elastic conditions. When the phase relationship of the vibration sources is uncertain, the upper and lower envelope values ​​of the superposition response power spectral density are determined based on the cross-power spectral density constraint. Combining the frequency division bands used for precision instrument evaluation, the upper and lower envelopes of the effective values ​​of the superposition response within each frequency band are calculated, yielding the frequency division prediction envelope interval of the micro-vibration superposition response under multi-source action. This invention, by characterizing the multi-source superposition response and its uncertainties through frequency division, realizes the prediction of the micro-vibration response range in the environment of precision instruments, providing a basis for precision instrument layout, vibration evaluation, and vibration control.

Description

Technical Field

[0001] This invention relates to the field of micro-vibration prediction and evaluation technology for engineering structures, and in particular to a method, system and storage medium for predicting the frequency division of micro-vibration superposition response in multi-vibration source environments for precision instruments. Background Technology

[0002] With the rapid development of high-end manufacturing, precision measurement, semiconductor processing, medical imaging, and nanoscale experimental testing, precision instruments and high-end manufacturing equipment such as electron microscopes, lithography machines, precision measuring devices, and medical imaging systems are increasingly being installed inside industrial buildings, research buildings, or multi-story factories. These precision instruments are extremely sensitive to micro-vibrations in their operating environment. When the structural vibration response exceeds the instrument's permissible limits, it can easily cause blurred imaging, positioning deviations, decreased processing accuracy, increased measurement errors, and even affect the long-term stable operation of the equipment. Therefore, in the process of precision instrument placement, factory design, structural vibration control, and operation and maintenance, it is necessary to predict and evaluate the micro-vibration response at the target location.

[0003] In real-world engineering environments, the building structures housing precision instruments are typically not subjected to a single vibration source, but rather simultaneously influenced by road traffic, rail traffic, power equipment operation, and other environmental vibration sources. Different vibration sources differ in excitation frequency, duration, propagation path, operating conditions, and time-varying characteristics, resulting in structural vibration responses at the target response point exhibiting characteristics of multi-frequency components, multi-source superposition, and uncertain variations. Especially when the frequency components of different vibration sources overlap, the superimposed response is not simply the sum of the energies of the individual source responses. The correlation and phase relationship between the responses of different sources may enhance the superimposed response within a local frequency range, or it may cancel out the superimposed response within a local frequency range.

[0004] Existing methods for predicting or evaluating micro-vibrations typically focus on structural response analysis under single vibration sources, or on superimposing the response results of multiple sources in a deterministic manner. These methods are applicable when the phase relationships between the vibration sources are known or their spectra do not significantly overlap. However, when multiple sources act together and their frequency bands overlap, it is difficult to reasonably characterize the impact of phase uncertainties between sources on the superimposed response. Ignoring the cross-spectral terms between the responses of different sources may underestimate or overestimate the true micro-vibration level at the target response point; conversely, directly using a conservative superposition method may lead to overly conservative prediction results, which is detrimental to the rational formulation of precision instrument placement and vibration control schemes.

[0005] On the other hand, the evaluation of micro-vibration in the operating environment of precision instruments usually does not focus solely on the response at a single frequency point, but rather on the effective value of the response within a specific frequency band. Different precision instruments have different permissible vibration requirements in different frequency ranges. Therefore, the prediction results of the structural micro-vibration response under multiple vibration sources need to reflect the range of response variation within the frequency bands. Existing methods, if they only provide a single, definitive value of the total response, are insufficient to reveal the range of response fluctuations caused by the overlap of vibration source spectra and phase uncertainties within different frequency bands, and also fail to provide a prediction interval in the sense of frequency division for the environmental evaluation of precision instruments.

[0006] Therefore, it is necessary to propose a frequency division prediction method for the superposition response of micro-vibrations in multi-source environments of precision instruments. Based on obtaining the power spectral density of the response of each single source, the method considers the influence of cross-spectral terms and phase uncertainties under different source spectral overlap conditions, constructs the upper and lower envelopes of the power spectral density of the superposition response of multiple sources, and further obtains the prediction envelope interval of the effective value of the superposition response within the target frequency division band. This provides a more reasonable technical basis for the evaluation of micro-vibrations in multi-source environments of precision instruments. Summary of the Invention

[0007] Based on this, it is necessary to address the problems of difficulty in accurately predicting the superimposed micro-vibration response of precision instruments under multiple vibration sources, difficulty in characterizing the phase uncertainty when the vibration source spectra overlap, and difficulty in determining the response range within the frequency division band. Therefore, a frequency division prediction method, system, and storage medium for the superimposed micro-vibration response of precision instruments in multi-vibration source environments should be proposed.

[0008] To achieve the above objectives, in a first aspect, this application provides a method for frequency division prediction of micro-vibration superposition response in multi-vibration-source environments for precision instruments, the method comprising:

[0009] Obtain the structural vibration response at the target response point under the action of several single vibration sources, and determine the response power spectral density corresponding to each single vibration source; Based on the linear superposition relationship of structural vibration response under multiple vibration sources, a frequency domain expression of the power spectral density of the superimposed response of multiple vibration sources is established. The frequency domain expression includes the autospectral terms formed by the power spectral density of each single vibration source response and the cross-spectral terms formed between different single vibration source responses. At frequencies where the spectra of different single sources overlap, the phase difference between the responses of different single sources is taken as an uncertainty, and the range of values ​​of the cross-spectral term is determined based on the cross-power spectral density constraint relationship. Based on the value ranges of the self-spectral term and the cross-spectral term, the upper and lower envelope values ​​of the power spectral density of the multi-source superposition response are constructed. Based on the upper and lower envelope values ​​of the power spectral density of the multi-source superposition response, calculate the upper and lower envelope values ​​of the effective superposition response within the target frequency band. Based on the upper envelope value and lower envelope value of the effective value of the superimposed response corresponding to each target frequency band, the frequency prediction envelope interval of the micro-vibration superimposed response at the target response point under the action of multiple vibration sources is obtained.

[0010] Optionally, obtaining the structural vibration response at the target response point under the action of several single vibration sources specifically includes: The structural vibration response at the target response point is obtained under the individual action of different vibration sources; the different vibration sources include at least two of the following: road traffic vibration sources, rail traffic vibration sources, and power equipment vibration sources; The structural vibration response is obtained through field testing at the target response point under the action of a single vibration source, or by applying the measured or constructed single vibration source excitation to the structural dynamic model for calculation.

[0011] Optionally, the establishment of a frequency domain expression for the power spectral density of the superimposed response of multiple vibration sources based on the linear superposition relationship of the structural vibration response under multiple vibration sources specifically includes: The structural vibration time history response at the target response point under multiple vibration sources is expressed as a linear superposition of the time history responses under each single vibration source. An autocorrelation function is constructed based on the vibration response of the structure, and the frequency domain expression of the power spectral density of the superimposed response of multiple vibration sources is obtained through Fourier transform. The frequency domain expression of the power spectral density of the multi-source superposition response is as follows:

[0012] In the formula, The power spectral density of the response from multiple vibration sources. For the first i Power spectral density of a single vibration source response For the first i The response of the single vibration source and the first j Cross-power spectral density between the responses of individual vibration sources Let be the phase difference between the response of the i-th vibration source and the response of the j-th vibration source at frequency . n This represents the number of single vibration sources.

[0013] Optionally, when the first i The single vibration source and the first j A single vibration source at frequency f When effective energy components are present at all points, the first... i The response of the single vibration source and the first j The cross-power spectral density between the responses of individual vibration sources is expressed as:

[0014] In the formula, is the modulus of the cross-power spectral density.

[0015] Optionally, the step of using the phase difference between different single-source responses as an uncertainty and determining the range of values ​​for the cross-spectral term based on the cross-power spectral density constraint relationship specifically includes: The phase difference As an uncertainty, and based on the cross-power spectral density constraint relationship, the range of values ​​for the real part of the cross-spectral term is determined as follows:

[0016] In the formula, For the first j Power spectral density of a single vibration source response.

[0017] Optionally, constructing the upper and lower envelope values ​​of the power spectral density of the multi-source superposition response based on the value ranges of the self-spectral term and the cross-spectral term specifically includes: Based on the power spectral density of each individual vibration source response and the range of the cross-spectral term, the envelope value of the power spectral density of the multi-source superposition response is constructed:

[0018] And the envelope value under the power spectral density of the multi-source superposition response:

[0019] Furthermore, the power spectral density of the superimposed response from multiple vibration sources satisfy:

[0020] In the formula, The envelope value of the power spectral density of the multi-source superposition response. This represents the envelope value under the power spectral density of the superimposed response from multiple vibration sources.

[0021] Optionally, the step of calculating the upper envelope value and lower envelope value of the effective superposition response within the target frequency band based on the upper and lower envelope values ​​of the power spectral density of the multi-source superposition response specifically includes: Determine the first k The frequency range corresponding to each target frequency band; Within the specified frequency range, the envelope values ​​of the power spectral density of the multi-source superposition response are integrated in the frequency band or discretely accumulated to obtain the first... k The envelope value of the superimposed effective value of the target frequency band; Within the specified frequency range, the envelope value under the power spectral density of the multi-source superposition response is integrated in the frequency band or discretely accumulated to obtain the first... k The envelope value of the superimposed response effective value corresponding to each target frequency band.

[0022] Optionally, the target frequency band is a 1 / 3 octave band, the first... k The set of discrete frequency points corresponding to each target frequency band for:

[0023] In the formula, For discrete frequency points, For the first k The lower limit frequency of each target frequency band. For the first k The upper limit frequency of each target frequency band; Then the first k The upper envelope value and lower envelope value of the effective superposition response corresponding to each target frequency band are as follows:

[0024]

[0025] In the formula, For the first k The envelope value of the superimposed effective value of the target frequency band. For the first k The envelope value of the superimposed response RMS value corresponding to each target frequency band. For discrete frequency resolution; The first k The frequency division prediction envelope interval corresponding to each target frequency division band is:

[0026] For all K By repeatedly calculating the frequency bands of each target, the set of frequency-division prediction envelope intervals of the superimposed micro-vibration response of the structure at the target response point under the action of multiple vibration sources is obtained:

[0027] In the formula, It is the set of frequency division prediction envelope intervals for the superimposed micro-vibration response of the structure at the target response point under the action of multiple vibration sources.

[0028] Secondly, this application also provides a micro-vibration superposition response frequency division prediction system for multi-vibration source environment of precision instruments, which is used to implement the micro-vibration superposition response frequency division prediction method for multi-vibration source environment of precision instruments described in the first aspect. It includes: a single vibration source response acquisition unit, a frequency domain expression establishment unit, a phase uncertainty envelope construction unit, and a frequency division prediction unit. The single vibration source response acquisition unit is used to acquire the structural vibration response at the target response point under the action of several single vibration sources, and to determine the response power spectral density corresponding to each single vibration source. The frequency domain expression establishment unit is used to establish a frequency domain expression of the power spectral density of the superimposed response of multiple vibration sources based on the linear superposition relationship of the structural vibration response under the action of multiple vibration sources. The phase uncertainty envelope construction unit is used to take the phase difference between the responses of different single sources as an uncertainty at frequencies where the spectra of different single sources overlap, and to construct the upper and lower envelope values ​​of the power spectral density of the superimposed response of multiple sources based on the cross power spectral density constraint relationship. The frequency division prediction unit is used to calculate the upper envelope value and lower envelope value of the effective value of the superimposed response within the target frequency division band based on the upper and lower envelope values ​​of the power spectral density of the multi-source superimposed response, and to obtain the frequency division prediction envelope interval of the micro-vibration superimposed response at the target response point under the action of multiple vibration sources.

[0029] Thirdly, this application also provides a readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the steps of the method described in the first aspect.

[0030] The embodiments of the present invention have the following beneficial effects: This invention does not simply perform deterministic superposition of the responses of multiple single sources, but decomposes the power spectral density of the superimposed response of multiple sources into autospectral terms and crossspectral terms in the frequency domain, and introduces phase difference uncertainty when the spectra of different single sources overlap, thereby being able to characterize the enhancement or cancellation effects that may occur between different sources.

[0031] This invention constructs the upper and lower envelope values ​​of the power spectral density of the superimposed response of multiple vibration sources based on the mutual power spectral density constraint relationship, so that even when the phase relationship of different vibration sources is unknown or difficult to determine accurately, the prediction range of the structural micro-vibration response at the target response point can still be obtained.

[0032] This invention further converts the upper and lower envelopes of the power spectral density into the upper and lower envelopes of the effective values ​​of the superimposed response within the target frequency band, thereby obtaining the micro-vibration prediction envelope interval in the sense of frequency division, which is suitable for the needs of vibration evaluation and control by frequency band in the environment of precision instrument use.

[0033] This invention establishes a complete calculation process for structural micro-vibration response under multi-source conditions, from single-source data to frequency-based prediction results, by acquiring the power spectral density of single-source response, establishing frequency domain expression, constructing uncertainty envelope, and outputting frequency division prediction intervals. This provides a technical basis for precision instrument placement, structural micro-vibration evaluation, and vibration control scheme formulation. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] in: Figure 1 This is a schematic diagram of a micro-vibration superposition response frequency division prediction method for multi-vibration source environments of precision instruments in one embodiment. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them; all other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0037] The following description provides specific calculation steps and expressions to facilitate understanding of the technical solution proposed by this invention; however, it will be apparent to those skilled in the art that this invention can be implemented without one or more specific details. Unless otherwise specified, the following embodiments and the technical features described therein can be combined with each other.

[0038] This invention provides a frequency division prediction method for the superposition response of micro-vibrations in multi-source environments for precision instruments. It is applicable to the prediction and evaluation of micro-vibrations at target response points of building structures under the combined action of multiple types of environmental vibration sources. These multiple types of environmental vibration sources may include road traffic vibration sources, rail traffic vibration sources, power equipment vibration sources, and other vibration sources capable of causing micro-vibration responses in building structures. The target response point can be the proposed location of the precision instrument, its existing location, or a structural measuring point requiring micro-vibration evaluation.

[0039] The basic idea of ​​this invention is that, under micro-vibration conditions, the structural response amplitude is small, and the structure can be approximated as being in a linear elastic working state. Therefore, the structural response under multiple vibration sources can be expressed as a linear superposition of the responses of each individual vibration source. However, in the frequency domain, the power spectral density of the multi-source superposition response includes not only the autospectral terms of each individual vibration source response but also the cross-spectral terms between different individual vibration source responses. When different vibration sources have spectral overlap at the same frequency, the magnitude and sign of the cross-spectral terms are affected by the phase difference of the vibration source responses. Since the phase relationship between different vibration sources is usually difficult to determine accurately in engineering practice, this invention treats the phase difference as an uncertainty and constructs the upper and lower envelopes of the power spectral density of the multi-source superposition response based on the cross-power spectral density constraint relationship, further obtaining the predicted envelope interval of the effective value of the superposition response within each target frequency band.

[0040] like Figure 1 As shown, in one embodiment, a method for frequency division prediction of micro-vibration superposition response in multi-vibration-source environments for precision instruments is provided. The method includes steps S101 to S106, which are detailed below: Step S101: Obtain the structural vibration response at the target response point under the action of several single vibration sources, and determine the response power spectral density corresponding to each single vibration source.

[0041] The purpose of step S101 is to obtain the structural vibration response at the target response point under the individual action of various single vibration sources, and to convert the response of each single vibration source from the time domain to the frequency domain through power spectral density estimation, so as to provide basic input data for the frequency domain analysis of the subsequent multi-source superposition response.

[0042] In some embodiments, the single vibration source can be a road traffic vibration source, a rail transit vibration source, a power equipment vibration source, or other environmental vibration sources. For ease of explanation, let's assume a common source. n The single vibration source, the first i The structural vibration response at the target response point under the action of a single vibration source is denoted as . .

[0043] In some embodiments, the first i The structural vibration response at the target response point under the action of a single vibration source can be obtained through field testing. For example, under conditions where the influence of other vibration sources is weak or can be isolated, the acceleration, velocity, or displacement response signal at the target response point can be collected when a single vibration source acts alone.

[0044] In other embodiments, the first i The structural vibration response at the target response point under the action of a single vibration source can also be obtained through structural dynamic model calculation. For example, by applying a measured or constructed single vibration source as input excitation to the structural dynamic model, the structural vibration response at the target response point can be calculated.

[0045] Furthermore, when the object of engineering analysis is a discrete signal, the first... i The discrete response sequence at the target response point under the action of a single vibration source can be expressed as:

[0046] In some embodiments, the power spectral density of the discrete response sequence can be estimated to obtain the first... i The power spectral density of the response of a single vibration source Power spectral density estimation methods can include the Welch method or other power spectral estimation methods suitable for engineering vibration signal analysis.

[0047] Specifically, when using the Welch method, the discrete response sequence can be divided into several overlapping data segments. A window function is applied to each data segment, and the periodograms corresponding to each data segment are averaged to obtain the power spectral density of the single-source response. The purpose of this step is to obtain the contribution of each single source to the structural vibration energy at the target response point at different frequencies, providing input for the subsequent construction of the multi-source superposition response envelope.

[0048] It should be noted that the power spectral density estimation method is not the only limiting method of this invention. As long as the response power spectral density at the target response point under the action of each single vibration source can be obtained, it can be used for subsequent calculations in this invention.

[0049] Step S102: Based on the linear superposition relationship of the structural vibration response under multiple vibration sources, establish the frequency domain expression of the power spectral density of the superimposed response of multiple vibration sources. The frequency domain expression includes the autospectral terms formed by the power spectral densities of each individual vibration source response and the cross-spectral terms formed between the responses of different individual vibration sources.

[0050] The purpose of step S102 is to decompose the total response power spectral density under the combined action of multiple vibration sources into the spectral terms of each individual vibration source and the cross-spectral terms between different vibration sources, based on the principle of linear superposition of structural response under linear elastic conditions, thereby establishing a complete frequency domain expression framework for the superposition response power spectral density of multiple vibration sources.

[0051] Specifically, under micro-vibration conditions, the structural response amplitude is small, and the structure can be approximated as being in a linear elastic working state. Based on this condition, it can be assumed that the structural vibration response at the target response point under the combined action of multiple single vibration sources satisfies a linear superposition relationship. Therefore, the structural vibration time history response at the target response point under the action of multiple vibration sources can be expressed as a linear superposition of the time history responses under the action of each single vibration source, that is: (1) In the formula, This represents the structural vibration response at the target response point under multiple vibration sources. For the first iStructural vibration response at the target response point under the action of a single vibration source n This represents the number of single vibration sources.

[0052] Furthermore, an autocorrelation function is constructed based on the structural vibration response, and the frequency domain expression of the power spectral density of the multi-source superposition response is obtained through Fourier transform.

[0053] Specifically, the structural vibration response at the target response point under multiple vibration sources is considered as a random process, and its autocorrelation function... It can be represented as: (2) Among them, E[ ] represents the mathematical expectation. τ This is the time shift.

[0054] Substitute equation (1) into equation (2) and define the first... i The response of the single vibration source and the first j The cross-correlation function between the responses of individual vibration sources can be used to obtain the autocorrelation function of the superimposed response of multiple vibration sources, which is composed of the autocorrelation functions of the responses of each individual vibration source and the cross-correlation function between the responses of different individual vibration sources.

[0055] For the autocorrelation function Performing a Fourier transform yields the frequency domain expression of the power spectral density of the superimposed response from multiple vibration sources: (3) In the formula, The power spectral density of the response from multiple vibration sources. For the first i Power spectral density of a single vibration source response For the first i The response of the single vibration source and the first j The cross-power spectral density between the responses of individual vibration sources, Re[ [] indicates taking the real part.

[0056] In the above scheme, the power spectral density of the structural vibration response under multiple vibration sources consists of two parts: one part is the autospectral term of the structural vibration response under the action of each single vibration source, reflecting the energy contributed by each vibration source individually; the other part is the cross-spectral term, reflecting the correlation between different vibration sources at the same frequency. When different vibration sources simultaneously have significant energy components at a certain frequency, their superposition response may enhance or cancel each other out.

[0057] Step S103: At frequencies where the spectra of different single sources overlap, the phase difference between the responses of different single sources is taken as an uncertainty, and the range of values ​​of the cross-spectral term is determined based on the cross-power spectral density constraint relationship.

[0058] The function of step S103 is to: after identifying the frequency ranges where different single source spectra overlap, take the phase difference between the source responses as an uncertainty, and determine the value boundary of the cross spectrum term based on the cross power spectral density constraint relationship, thereby transforming the phase relationship between sources that is difficult to determine in engineering into a calculable value range.

[0059] In some embodiments, when the first i The single vibration source and the first j A single vibration source satisfies the following within the frequency range Ω: (4) Then determine the first i The single vibration source and the first j The single vibration sources have spectral overlap within the frequency range Ω; that is, the first... i The response of the single vibration source and the first j The response of a single vibration source at frequency f Effective energy components are present at all locations. In this case, the first... i The response of the single vibration source and the first j The cross-power spectral density between the responses of individual vibration sources is expressed as:

[0060] In the formula, These are the cross-spectral modes, i.e., the modes of the cross-power spectral density; For the first i The response of the vibration source and the first j The response of each vibration source at frequency f The phase difference at that point.

[0061] In signal processing, any complex number (cross-power spectral density) Any complex number can be expressed as its modulus multiplied by a phase factor. According to Euler's formula, the real part of this complex number is equal to the modulus multiplied by the cosine of the phase difference, i.e.: (5) Then the expansion of equation (3) can be expressed as: (6) Equation (6) and Equation (3) are completely equivalent.

[0062] In real-world engineering environments, the operating conditions of vibration sources such as road traffic, rail transit, and power equipment are typically random and time-varying, making it difficult to accurately determine the phase relationship between different vibration sources. Therefore, in this embodiment of the invention, the phase difference is treated as an uncertainty. This approach avoids directly providing a single, definitive multi-source superposition response result when the phase relationship is unknown.

[0063] Step S104: Based on the value ranges of the self-spectral term and the cross-spectral term, construct the upper envelope value and lower envelope value of the power spectral density of the multi-source superposition response.

[0064] The purpose of step S104 is to construct the upper and lower envelope values ​​of the power spectral density of the multi-source superposition response based on the value ranges of the self-spectral term in step S102 and the cross-spectral term in step S103, so that the power spectral density of the superposition response is within the range formed by the upper and lower envelope values ​​at each frequency, thereby reflecting the possible range of the multi-source superposition response.

[0065] Specifically, based on the fundamental inequality of cross-power spectral density, we can obtain: (7) Combined with phase difference The uncertainty will affect the phase difference. As an uncertain quantity, and based on the cross-power spectral density constraint relationship, the range of values ​​for the real part of the cross-spectral term can be determined: (8) Based on the range of cross-spectral terms defined by equation (8), the upper and lower envelope values ​​of the power spectral density of the superimposed response of multiple vibration sources can be constructed.

[0066] Specifically, firstly, based on the power spectral density of each individual vibration source response and the range of the cross-spectral term, the envelope value of the power spectral density of the multi-source superposition response is constructed: (9) When different single-source responses are at frequency f When the behavior is in the extreme condition of in-phase superposition, the power spectral density of the multi-source superposition response obtains the upper envelope value.

[0067] Secondly, based on the power spectral density of each single vibration source response and the range of the cross-spectral term, the envelope value under the superimposed power spectral density of multiple vibration sources is constructed: (10) When different single-source responses are at frequency f When the behavior is exhibited as an antiphase superposition extreme condition, the lower envelope value of the power spectral density of the multi-source superposition response is obtained.

[0068] Furthermore, the power spectral density of the multi-source superposition response satisfy: (11) The above formula shows that at frequency fAt a given frequency, the power spectral density of the superimposed response under multiple vibration sources is not a uniquely determined value, but rather lies within a range defined by the upper and lower envelope values. The width of this range reflects the degree to which phase uncertainty affects the power spectral density of the superimposed response. If the envelope range is wide at a certain frequency, it indicates that different vibration sources significantly overlap at that frequency, and phase changes cause significant response fluctuations. If the envelope range is narrow, it indicates that the superimposed response at that frequency is not sensitive to phase changes, or is dominated by a single vibration source.

[0069] Step S105: Calculate the upper envelope value and lower envelope value of the effective value of the superimposed response within the target frequency band based on the upper and lower envelope values ​​of the power spectral density of the multi-source superposition response.

[0070] The purpose of step S105 is to convert the upper and lower envelope values ​​of the power spectral density of the multi-source superposition response obtained in step S104 into upper and lower envelope values ​​of the effective values ​​of the superposition response in each frequency band by performing frequency band integration or discrete accumulation according to the target frequency band, so that the prediction results can be adapted to the actual needs of frequency band analysis in the evaluation of precision instruments.

[0071] Specifically, the evaluation of micro-vibration in the operating environment of precision instruments typically focuses on the effective value of the response within a specific frequency band, rather than just a single frequency point. Therefore, after obtaining the upper and lower envelope values ​​of the power spectral density of the multi-source superimposed response, it is necessary to further convert them into the envelope of the effective value of the superimposed response within the target frequency band.

[0072] In some embodiments, the target frequency band can be a 1 / 3 octave band. Let the... k The set of discrete frequency points corresponding to each target frequency band is: (12) In the formula, For discrete frequency points, For the first k The lower limit frequency of each target frequency band. For the first k The upper limit frequency of each target frequency band.

[0073] In the above scheme, the first k The upper envelope value and lower envelope value of the effective superposition response corresponding to each target frequency band are as follows: (13) (14) In the formula, For the first k The envelope value of the superimposed effective value of the target frequency band. For the first kThe envelope value of the superimposed response RMS value corresponding to each target frequency band. It represents the discrete frequency resolution.

[0074] It should be noted that the 1 / 3 octave band is only one preferred embodiment of the present invention. In other embodiments, the target frequency band can also be divided according to the vibration evaluation standards of precision instruments, the allowable vibration curve of the equipment, or the requirements of engineering analysis.

[0075] Step S106: Based on the upper envelope value and lower envelope value of the effective superposition response corresponding to each target frequency band, obtain the frequency prediction envelope interval of the micro-vibration superposition response at the target response point under the action of multiple vibration sources.

[0076] The purpose of step S106 is to combine the upper and lower envelopes of the effective values ​​corresponding to each target frequency band into a prediction envelope interval, thereby forming a complete frequency division prediction result of the superimposed micro-vibration response of the structure at the target response point under the action of multiple vibration sources, providing a basis for precision instrument layout, micro-vibration evaluation and vibration control.

[0077] In some embodiments, the first k The frequency division prediction envelope interval corresponding to each target frequency division band can be expressed as: (15) For all K By repeatedly calculating the frequency bands of each target, the set of frequency-division prediction envelope intervals of the superimposed micro-vibration response of the structure at the target response point under the action of multiple vibration sources is obtained: (16) Through the above steps, this invention can obtain the possible range of structural micro-vibration response values ​​at the target response point within each target frequency band, even when the phase relationships of different vibration sources are unknown. Compared to directly adding the power spectral densities of the responses of each single vibration source, this invention considers the cross-spectral terms and phase uncertainties between different vibration sources; compared to directly using a single conservative superposition result, this invention can simultaneously provide the upper and lower envelopes, thereby reflecting the uncertainty range of the multi-source superposition response.

[0078] In one embodiment, a micro-vibration superposition response frequency division prediction system for multi-source environments of precision instruments is also provided. This system is used to implement the above-mentioned micro-vibration superposition response frequency division prediction method for multi-source environments of precision instruments. The system includes: a single-source response acquisition unit, a frequency domain expression establishment unit, a phase uncertainty envelope construction unit, and a frequency division prediction unit.

[0079] The single vibration source response acquisition unit is used to acquire the structural vibration response at the target response point under the action of several single vibration sources, and to determine the response power spectral density corresponding to each single vibration source.

[0080] In some embodiments, the single-source response acquisition unit can receive single-source response data obtained from field tests, or it can receive single-source response data calculated from a structural dynamic model. The single-source response acquisition unit can also perform power spectral density estimation on the discrete response sequence to obtain the response power spectral density corresponding to each single source.

[0081] The frequency domain expression establishment unit is used to establish a frequency domain expression of the power spectral density of the superimposed response of multiple vibration sources based on the linear superposition relationship of the structural vibration response under multiple vibration sources.

[0082] Specifically, the frequency domain expression establishment unit is used to construct self-spectral terms based on the power spectral density of each single source response and to construct cross-spectral terms based on the cross-power spectral density between different single sources, thereby forming a multi-source superposition response power spectral density expression including self-spectral terms and cross-spectral terms.

[0083] The phase uncertainty envelope construction unit is used to construct the upper and lower envelope values ​​of the power spectral density of the superimposed response of multiple sources at frequencies where the spectra of different single sources overlap, taking the phase difference between the responses of different single sources as an uncertainty, and based on the cross power spectral density constraint relationship.

[0084] In some embodiments, the phase uncertainty envelope construction unit is used to determine whether there are effective energy components in the power spectral densities of different single-source responses at the target frequency; when there is spectral overlap, the phase uncertainty envelope construction unit can calculate the upper envelope value and the lower envelope value of the power spectral density respectively.

[0085] The frequency division prediction unit is used to calculate the upper envelope value and lower envelope value of the effective value of the superimposed response within the target frequency division band based on the upper and lower envelope values ​​of the power spectral density of the multi-source superimposed response, and to obtain the frequency division prediction envelope interval of the micro-vibration superimposed response at the target response point under the action of multiple vibration sources.

[0086] In some embodiments, the frequency division prediction unit is used to determine the frequency range or discrete frequency point set corresponding to each target frequency division band, and to integrate or discretely accumulate the upper envelope value and lower envelope value of the power spectral density within each target frequency division band, thereby obtaining the effective value envelope interval corresponding to each frequency band.

[0087] In one embodiment, a computer device is also provided, the computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the above-described method for predicting the frequency division of micro-vibration superposition response in a multi-vibration-source environment for precision instruments.

[0088] Specifically, the processor can perform the following steps: Obtain the structural vibration response at the target response point under the action of several single vibration sources, and determine the response power spectral density corresponding to each single vibration source; Based on the linear superposition relationship of structural vibration response under multiple vibration sources, a frequency domain expression of the power spectral density of the superposition response of multiple vibration sources is established. At frequencies where the spectra of different single sources overlap, the phase difference between the responses of different single sources is taken as an uncertainty, and the range of cross-spectral terms is determined based on the cross-power spectral density constraint relationship. Based on the range of values ​​for the self-spectral term and the cross-spectral term, the upper and lower envelope values ​​of the power spectral density of the superimposed response of multiple vibration sources are constructed. Based on the upper and lower envelope values, calculate the effective values ​​of the superposition response within the target frequency band, including the upper and lower envelope values. The frequency division prediction envelope interval is obtained based on the upper envelope value and lower envelope value of the superimposed effective value of the superimposed effective value of each target frequency division band.

[0089] In one embodiment, a readable storage medium is also provided, the readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps in the above method embodiments.

[0090] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by computer program instructions and related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the above method embodiments. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory.

[0091] In summary, this invention provides a method for predicting the frequency division of superimposed micro-vibration responses in multi-source environments for precision instruments. This method involves acquiring the power spectral density of a single vibration source response, establishing the frequency domain expression of the superimposed response of multiple vibration sources, constructing the power spectral density envelope under phase uncertainty, and outputting the predicted effective value interval for each frequency division. This method can provide the predicted envelope interval of the structural micro-vibration response at the target response point within different target frequency division bands, even when the spectra of different vibration sources overlap and the phase relationship is uncertain. This provides a basis for evaluating micro-vibration in the operating environment of precision instruments, optimizing equipment layout, and developing vibration control schemes.

Claims

1. A method for frequency division prediction of micro-vibration superposition response in multi-vibration-source environments for precision instruments, characterized in that, The method includes: Obtain the structural vibration response at the target response point under the action of several single vibration sources, and determine the response power spectral density corresponding to each single vibration source; Based on the linear superposition relationship of structural vibration response under multiple vibration sources, a frequency domain expression of the power spectral density of the superimposed response of multiple vibration sources is established. The frequency domain expression includes the autospectral terms formed by the power spectral density of each single vibration source response and the cross-spectral terms formed between different single vibration source responses. At frequencies where the spectra of different single sources overlap, the phase difference between the responses of different single sources is taken as an uncertainty, and the range of values ​​of the cross-spectral term is determined based on the cross-power spectral density constraint relationship. Based on the value ranges of the self-spectral term and the cross-spectral term, the upper and lower envelope values ​​of the power spectral density of the multi-source superposition response are constructed. Based on the upper and lower envelope values ​​of the power spectral density of the multi-source superposition response, calculate the upper and lower envelope values ​​of the effective superposition response within the target frequency band. Based on the upper envelope value and lower envelope value of the effective value of the superimposed response corresponding to each target frequency band, the frequency prediction envelope interval of the micro-vibration superimposed response at the target response point under the action of multiple vibration sources is obtained.

2. The method according to claim 1, characterized in that, The acquisition of the structural vibration response at the target response point under the action of several single vibration sources specifically includes: The structural vibration response at the target response point is obtained under the individual action of different vibration sources; the different vibration sources include at least two of the following: road traffic vibration sources, rail traffic vibration sources, and power equipment vibration sources; The structural vibration response is obtained through field testing at the target response point under the action of a single vibration source, or by applying the measured or constructed single vibration source excitation to the structural dynamic model for calculation.

3. The method according to claim 1, characterized in that, The frequency domain expression of the power spectral density of the superimposed response of the structure based on the linear superposition relationship of the vibration response under multiple vibration sources specifically includes: The structural vibration time history response at the target response point under multiple vibration sources is expressed as a linear superposition of the time history responses under each single vibration source. An autocorrelation function is constructed based on the vibration response of the structure, and the frequency domain expression of the power spectral density of the superimposed response of multiple vibration sources is obtained through Fourier transform. The frequency domain expression of the power spectral density of the multi-source superposition response is as follows: In the formula, The power spectral density of the superimposed response from multiple vibration sources. For the first i Power spectral density of a single vibration source response For the first i The response of the single vibration source and the first j Cross-power spectral density between the responses of individual vibration sources Let be the phase difference between the response of the i-th vibration source and the response of the j-th vibration source at frequency . n This represents the number of single vibration sources.

4. The method according to claim 3, characterized in that, When the i The single vibration source and the first j A single vibration source at frequency f When effective energy components are present at all points, the first... i The response of the single vibration source and the first j The cross-power spectral density between the responses of a single vibration source is expressed as: In the formula, is the modulus of the cross-power spectral density.

5. The method according to claim 4, characterized in that, The step of using the phase difference between different single-source responses as an uncertainty and determining the range of values ​​for the cross-spectral term based on the cross-power spectral density constraint relationship specifically includes: The phase difference As an uncertainty, and based on the cross-power spectral density constraint relationship, the range of values ​​for the real part of the cross-spectral term is determined as follows: In the formula, For the first j Power spectral density of a single vibration source response.

6. The method according to claim 5, characterized in that, The step of constructing the upper and lower envelope values ​​of the power spectral density of the multi-source superposition response based on the value ranges of the self-spectral term and the cross-spectral term specifically includes: Based on the power spectral density of each individual vibration source response and the range of the cross-spectral term, the envelope value of the power spectral density of the multi-source superposition response is constructed: And the envelope value under the power spectral density of the multi-source superposition response: Furthermore, the power spectral density of the superimposed response from multiple vibration sources satisfy: In the formula, The envelope value of the power spectral density of the multi-source superposition response. This represents the envelope value under the power spectral density of the superimposed response from multiple vibration sources.

7. The method according to claim 6, characterized in that, The step of calculating the upper and lower envelope values ​​of the effective superposition response within the target frequency band based on the upper and lower envelope values ​​of the power spectral density of the multi-source superposition response specifically includes: Determine the first k The frequency range corresponding to each target frequency band; Within the specified frequency range, the envelope values ​​of the power spectral density of the multi-source superposition response are integrated in the frequency band or discretely accumulated to obtain the first... k The envelope value of the superimposed effective value of the target frequency band; Within the specified frequency range, the envelope value under the power spectral density of the multi-source superposition response is integrated in the frequency band or discretely accumulated to obtain the first... k The envelope value of the superimposed response effective value corresponding to each target frequency band.

8. The method according to claim 7, characterized in that, The target frequency band is a 1 / 3 octave band, the first... k The set of discrete frequency points corresponding to each target frequency band for: In the formula, For discrete frequency points, For the first k The lower limit frequency of each target frequency band. For the first k The upper limit frequency of each target frequency band; Then the first k The upper envelope value and lower envelope value of the effective superposition response corresponding to each target frequency band are as follows: In the formula, For the first k The envelope value of the superimposed effective value of the target frequency band. For the first k The envelope value of the superimposed response RMS value corresponding to each target frequency band. For discrete frequency resolution; The first k The frequency division prediction envelope interval corresponding to each target frequency division band is: For all K By repeatedly calculating the frequency bands of each target, the set of frequency-division prediction envelope intervals of the superimposed micro-vibration response of the structure at the target response point under the action of multiple vibration sources is obtained: In the formula, It is the set of frequency division prediction envelope intervals for the superimposed micro-vibration response of the structure at the target response point under the action of multiple vibration sources.

9. A micro-vibration superposition response frequency division prediction system for multi-vibration source environments of precision instruments, characterized in that, The system includes: a single vibration source response acquisition unit, a frequency domain expression establishment unit, a phase uncertainty envelope construction unit, and a frequency division prediction unit; The single vibration source response acquisition unit is used to acquire the structural vibration response at the target response point under the action of several single vibration sources, and to determine the response power spectral density corresponding to each single vibration source. The frequency domain expression establishment unit is used to establish a frequency domain expression of the power spectral density of the superimposed response of multiple vibration sources based on the linear superposition relationship of the structural vibration response under the action of multiple vibration sources. The phase uncertainty envelope construction unit is used to take the phase difference between the responses of different single sources as an uncertainty at frequencies where the spectra of different single sources overlap, and to construct the upper and lower envelope values ​​of the power spectral density of the superimposed response of multiple sources based on the cross power spectral density constraint relationship. The frequency division prediction unit is used to calculate the upper envelope value and lower envelope value of the effective value of the superimposed response within the target frequency division band based on the upper and lower envelope values ​​of the power spectral density of the multi-source superimposed response, and to obtain the frequency division prediction envelope interval of the micro-vibration superimposed response at the target response point under the action of multiple vibration sources.

10. A readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it causes the processor to perform the steps of the method as described in any one of claims 1 to 8.

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