CN116127277B - Method and system for evaluating uncertainty of dynamic pressure measurement of shock wave flow field - Google Patents
Method and system for evaluating uncertainty of dynamic pressure measurement of shock wave flow field Download PDFInfo
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- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M9/00—Aerodynamic testing; Arrangements in or on wind tunnels
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- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L27/00—Testing or calibrating of apparatus for measuring fluid pressure
- G01L27/002—Calibrating, i.e. establishing true relation between transducer output value and value to be measured, zeroing, linearising or span error determination
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Abstract
The invention discloses a shock wave flow field dynamic pressure measurement uncertainty assessment method, which comprises the following steps: s1, decomposing a dynamic pressure measurement signal of a shock wave flow field to obtain a high-frequency noise component, a trend component, a ringing component and a low-frequency noise component; s2, expanding the sample size, and calculating the optimal estimated value of each component at each moment; s3, calculating the statistical mean value, the variance and the normal distribution of the optimal estimation value sequence of each component, estimating a probability density function according to a conjugated prior distribution rule, further obtaining a joint prior probability density function of data at each moment, and obtaining a joint posterior probability density function and posterior distribution statistics based on a likelihood function and a Bayesian method, further obtaining uncertainty of four components; and S4, synthesizing and calculating the uncertainty of the four components to obtain the dynamic pressure measurement expansion uncertainty of the shock wave flow field. The invention can realize uncertainty assessment of dynamic pressure measurement of the shock wave flow field with small sample and time-varying characteristics.
Description
Technical Field
The invention relates to the field of measurement and test, in particular to a method and a system for evaluating uncertainty of dynamic pressure measurement of a shock wave flow field.
Background
Shock wave flow fields are widely used in the fields of explosion testing, medical instruments, material impact testing, aeroengines and the like. In actual measurement, the dynamic pressure signal of the shock wave flow field generally has the characteristics of non-stability, nonlinearity, rapid frequency change and the like, and the repeatability of the measurement process is limited, so that the measurement result has typical small sample and time-varying characteristics, the reliability of the measurement uncertainty evaluation result is poor, and the measurement accuracy of the dynamic pressure of the shock wave flow field is seriously affected.
The most commonly used method for evaluating the uncertainty of the dynamic pressure measurement is a Bessel method, wherein the Bessel formula is adopted to calculate the standard deviation of the repeated measurement result of the dynamic pressure at each moment, and then the standard uncertainty and the expansion uncertainty of the measurement result of the dynamic pressure at each moment are evaluated respectively. The method has the advantages of simple calculation, small operand, no requirement on the distribution and frequency of dynamic pressure measurement data, and capability of rapidly obtaining the uncertainty of the dynamic pressure repetition measurement data of the shock wave flow field. However, the uncertainty evaluation process of the dynamic pressure measurement is poor in reliability due to the fact that the dynamic measurement data are calculated as a static process in the uncertainty evaluation process, and the interaction relation between the data at adjacent moments of the dynamic measurement result is ignored.
Aiming at the defects of the method, a dynamic measurement uncertainty assessment method based on the Bayesian theory appears, firstly, a priori probability density function of measured data is estimated according to probability distribution of repeated measured data, then a likelihood function of measured data at the later moment is constructed, a joint posterior probability density function of the measured data at the later moment is calculated based on the Bayesian theory, and finally, the dynamic measurement uncertainty is calculated according to the posterior probability distribution. When the method evaluates the uncertainty of the dynamic measurement, the dispersibility of the data at the current moment and the interaction relation between the data at the previous moment are comprehensively considered, and the uncertainty of the dynamic measurement can be evaluated more accurately. However, in the dynamic pressure measurement of the shock wave flow field, the sample size of the measurement result is usually very small, the repeated measurement result has the characteristic of a typical small sample, and the measurement uncertainty can cause inaccurate results when the Bayesian method is directly adopted to evaluate.
Disclosure of Invention
The invention mainly aims at the problem that the uncertainty of measurement cannot be reliably assessed due to the fact that a dynamic pressure measurement signal of a shock wave flow field is unstable and the sample size is small, and provides a method which is suitable for the conditions that the sample size of measurement data is small and the data change frequency is high, and can realize the uncertainty assessment of the dynamic pressure measurement of the shock wave flow field with small sample and time-varying characteristics.
The method and the system for evaluating the uncertainty of dynamic pressure measurement of the shock wave flow field can improve the accuracy of the result.
The technical scheme adopted by the invention is as follows:
the method for evaluating the uncertainty of dynamic pressure measurement of the shock wave flow field comprises the following steps:
s1, decomposing a dynamic pressure measurement signal of a shock wave flow field to obtain four components: a high frequency noise component, a trend component, a ringing component, and a low frequency noise component;
s2, respectively expanding sample size of the extracted four components, and calculating an optimal estimated value of each component at each moment of data;
s3, calculating a statistical mean value, a statistical variance and normal distribution of the optimal estimation value sequence of each component, estimating a probability density function according to a conjugated prior distribution rule, further obtaining a joint prior probability density function of data at each moment, and obtaining a joint posterior probability density function and posterior distribution statistics based on a likelihood function and a Bayesian method, further obtaining uncertainty of each component;
and S4, synthesizing and calculating the uncertainty of the four components to obtain the dynamic pressure measurement expansion uncertainty of the shock wave flow field.
In connection with the above technical solution, step S1 includes the following steps:
s11, decomposing a dynamic pressure measurement signal of the shock wave flow field by utilizing variation modal decomposition to obtain a series of narrow-band eigenmode functions, and extracting the narrow-band eigenmode functions with the center frequency higher than the ringing frequency to obtain a high-frequency noise component;
s12, reconstructing the rest narrow-band eigenmode functions, decomposing the reconstructed signals into a plurality of local oscillation mode functions by using empirical mode decomposition, and decomposing the local oscillation mode functions into a trend component, a ringing component and a low-frequency noise component; wherein the trend component is the eigenmode function with the lowest frequency; the eigenmode function of the ringing energy loss rate smaller than a certain threshold is the ringing component, otherwise is the low-frequency noise component.
In step S2, a self-service resampling method is specifically adopted to expand the sample size of the four extracted components.
In step S5, the arithmetic square root of uncertainty of four components is calculated, and then multiplied by an expansion coefficient to obtain the expansion uncertainty of dynamic pressure measurement of the shock wave flow field.
With the above technical solution, step S2 specifically includes:
s21, repeatedly measuring dynamic pressure of the shock wave flow field for M times, extracting to obtain a component matrix, and rewriting the component matrix into a form of a group of column vectors;
s22, carrying out equal probability on each column of vectors in the component matrix by adopting a self-help method, and resampling for a plurality of times to obtain self-help sample vectors, and calculating the average value of the self-help sample vectors;
s23, repeating the self-help sampling process for the self-help sample vector for a plurality of times to obtain a plurality of self-help samples, and calculating a large sample mean value sequence;
s24, sequencing and segmenting the large sample mean value sequence by adopting a statistical histogram method, and calculating an optimal estimated value.
The invention also provides a shock wave flow field dynamic pressure measurement uncertainty evaluation system, which comprises:
the signal decomposition module is used for decomposing the dynamic pressure measurement signal of the shock wave flow field to obtain four components: a high frequency noise component, a trend component, a ringing component, and a low frequency noise component;
the sample size expansion module is used for respectively carrying out sample size expansion on the four extracted components and calculating the optimal estimated value of the data of each component at each moment;
the standard uncertainty calculation module is used for calculating the statistical mean value, the variance and the normal distribution of the optimal estimation value sequence of each component, estimating a probability density function according to the conjugated prior distribution rule, further obtaining a joint prior probability density function of data at each moment, obtaining a joint posterior probability density function and posterior distribution statistic based on a likelihood function and a Bayesian method, and further obtaining the uncertainty of each component;
and the signal uncertainty calculation module is used for carrying out synthesis calculation on the uncertainties of the four components to obtain the expansion uncertainty of the dynamic pressure measurement of the shock wave flow field.
The signal decomposition module is specifically used for decomposing the dynamic pressure measurement signal of the shock wave flow field by utilizing variation modal decomposition to obtain a series of narrow-band eigenmode functions, and extracting the narrow-band eigenmode functions with the center frequency higher than the ringing frequency to obtain a high-frequency noise component; reconstructing the rest narrow-band eigenmode functions, decomposing the reconstructed signals into a plurality of local oscillation mode functions by using empirical mode decomposition, and decomposing the local oscillation mode functions into a trend component, a ringing component and a low-frequency noise component; wherein the trend component is the eigenmode function with the lowest frequency; the eigenmode function of the ringing energy loss rate smaller than a certain threshold is the ringing component, otherwise is the low-frequency noise component.
By adopting the technical scheme, the sample size expansion module specifically adopts a self-service resampling method to expand the sample size of the four extracted components.
The sample size expansion module is specifically used for repeatedly measuring the dynamic pressure of the shock wave flow field for M times, extracting to obtain a component matrix, and rewriting the component matrix into a form of a group of column vectors; the self-help method is adopted to carry out equal probability on each column of vectors in the component matrix, resampling can be carried out for a plurality of times, self-help sample vectors are obtained, and the average value of the self-help sample vectors is calculated; repeating the self-help sampling process for a plurality of times on the self-help sample vector to obtain a plurality of self-help samples, and calculating a large sample mean value sequence; and sequencing and segmenting the large sample mean value sequence by adopting a statistical histogram method, and calculating an optimal estimated value.
The invention also provides a computer storage medium, in which a computer program executable by a processor is stored, and the computer program executes the shock wave flow field dynamic pressure measurement uncertainty assessment method according to the technical scheme.
The invention has the beneficial effects that: the uncertainty evaluation method for measuring the dynamic pressure of the shock flow field of the invention decomposes the signal into a trend component, a ringing component, a low-frequency noise component and a high-frequency noise component, expands the sample size, calculates the uncertainty of the dynamic pressure measurement signal of the shock flow field based on a likelihood function and a Bayesian method, is suitable for the conditions of small sample size and high data change frequency of the dynamic pressure measurement data of the shock flow field, and can realize the uncertainty evaluation of the dynamic pressure measurement of the shock flow field with small sample and time-varying characteristics.
Further, the central frequency of the eigen mode function is compared with the ringing frequency of the dynamic pressure measurement signal of the shock wave flow field by combining the variation mode decomposition and the empirical mode decomposition algorithm, and the ringing energy loss rate index is introduced to realize the extraction of a trend component, a low-frequency noise component, a ringing component and a high-frequency noise component in the dynamic pressure measurement signal of the shock wave flow field.
Further, the method aims at the problems of complex dynamic pressure measurement process of the shock wave flow field, long single measurement time and low repeated measurement times caused by high cost, and adopts a self-help resampling method to expand sample sizes of the extracted trend component, ringing component, low-frequency noise component and high-frequency noise component respectively, so that the influence of the problem of small data sample sizes on the reliability of the evaluation result of the uncertainty of the dynamic pressure measurement of the shock wave flow field is reduced.
Further, aiming at the trend component, the ringing component, the low-frequency noise component and the high-frequency noise component after self-service resampling, according to the characteristic that repeated measurement data at any moment after the resampling is subjected to normal distribution, based on the conjugate prior Bayesian theory, the reliable evaluation of the time-varying uncertainty of each component is realized, and the dynamic pressure measurement uncertainty evaluation result of the shock wave flow field is obtained through synthesis. The synthesized uncertainty evaluation result not only characterizes the repeatability of shock dynamic pressure measurement, but also contains the interactive relation between the data of adjacent moments of the measurement signals, and has innovation in the field of time-varying uncertainty evaluation.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for evaluating uncertainty of dynamic pressure measurement of a shock wave flow field according to an embodiment of the invention;
FIG. 2 is a schematic diagram of a shock flow field dynamic pressure repeating 5 times measurement signal according to an embodiment of the present invention;
fig. 3 (a) -3 (e) are schematic diagrams showing the multi-component extraction results of the dynamic pressure repeating 5 times measurement signal according to the embodiment of the present invention;
FIG. 4 is a graph showing the multi-component measurement standard uncertainty assessment results according to an embodiment of the present invention;
fig. 5 is a graph showing the dynamic pressure measurement expansion uncertainty assessment result of the shock wave flow field according to the embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The invention mainly aims at solving the problem that the measurement uncertainty cannot be reliably assessed due to the fact that a dynamic pressure measurement signal of a shock wave flow field is unstable and the sample size is small, and provides a method for assessing the measurement uncertainty of the dynamic pressure of the shock wave flow field, as shown in fig. 1, the method comprises the following steps:
s1, decomposing a dynamic pressure measurement signal of a shock wave flow field to obtain four components: a high frequency noise component, a trend component, a ringing component, and a low frequency noise component;
s2, respectively expanding sample size of the extracted four components, and calculating an optimal estimated value of each component at each moment of data;
s3, calculating a statistical mean value, a statistical variance and normal distribution of the optimal estimation value sequence of each component, estimating a probability density function according to a conjugated prior distribution rule, further obtaining a joint prior probability density function of data at each moment, and obtaining a joint posterior probability density function and posterior distribution statistics based on a likelihood function and a Bayesian method, further obtaining uncertainty of each component;
and S4, synthesizing and calculating the uncertainty of the four components to obtain the dynamic pressure measurement expansion uncertainty of the shock wave flow field.
Wherein, the multi-component extraction of the dynamic pressure measurement signal in step S1 mainly comprises the following steps:
s11, decomposing a dynamic pressure measurement signal of the shock wave flow field by utilizing variation modal decomposition to obtain a series of narrow-band eigenmode functions, and extracting the narrow-band eigenmode functions with the center frequency higher than the ringing frequency to obtain a high-frequency noise component;
s12, reconstructing the rest narrow-band eigenmode functions, decomposing the reconstructed signals into a plurality of local oscillation mode functions by using empirical mode decomposition, and decomposing the local oscillation mode functions into a trend component, a ringing component and a low-frequency noise component; wherein the trend component is the eigenmode function with the lowest frequency; the eigenmode function of the ringing energy loss rate smaller than a certain threshold is the ringing component, otherwise is the low-frequency noise component.
The embodiment compares the center frequency of the eigenmode function with the ringing frequency of the dynamic pressure measurement signal of the shock wave flow field by combining the variation mode decomposition and the empirical mode decomposition algorithm, and introduces the ringing energy loss rate index to realize the extraction of the trend component, the low-frequency noise component, the ringing component and the high-frequency noise component in the dynamic pressure measurement signal of the shock wave flow field.
Specifically, it is assumed that the dynamic pressure measurement signal of the shock wave flow field isx(t) Adopts variational modal decomposition pairx(t) Decomposing to obtain a series of narrowband eigenmode functions, which are expressed as:
in the method, in the process of the invention,x（t) Dynamic pressure measurement signals of the shock wave flow field; BLIMF%t) Is a narrow-band eigenmode function;Kis the number of the narrow-band eigenmode functions.
Calculating the center frequency of each eigenmode functionf k （k=1,2，…K) And compares the center frequency of each eigenmode functionf k Dynamic pressure measuring signal ringing frequency of shock wave flow fieldf r Is of a size of (a) and (b). When the center frequency isf k Ringing frequency greater than dynamic pressure measurement signalf r When in use, the BLIMF ist) The high-frequency noise component is determined. Will satisfyf k ≤f r All BLIMF @ oft) Adding to obtain a reconstructed signalx r （t）。
Reconstructing a signal using empirical mode decompositionx r （t) Adaptive decomposition intodEach eigenmode function, expressed as
In the process, IMF is%t) Is an eigenmode function, the frequency of which is changed from high to low, and finally the IMF is extractedt) The lowest frequency is identified as the trend component.
To get from the rest IMFt) The intermediate separation ringing component and low-frequency noise component, and the introduction ringing energy loss rate index is defined as
In the method, in the process of the invention,A i andA 0 respectively the firstiIndividual IMFs and reconstructed signalsx r （t) Spectral amplitude at ringing frequency. When (when)E i < 10%, corresponding IMF i （t) Is identified as a ringing component and otherwise as a low frequency noise component.
The steps are implemented on each shock wave flow field dynamic pressure measurement signal, so that the extraction of a trend component, a ringing component, a low-frequency noise component and a high-frequency noise component can be realized.
Aiming at the problems of complex dynamic pressure measurement process of the shock wave flow field, long single measurement time and low repeated measurement times caused by high cost, a self-help resampling method can be adopted to expand sample sizes of extracted trend components, ringing components, low-frequency noise components and high-frequency noise components respectively, so that the influence of the problem of small data sample sizes on the reliability of the evaluation result of the uncertainty of the dynamic pressure measurement of the shock wave flow field is reduced.
The multi-component data sample size expansion in step S2 mainly includes the steps of:
assume that a certain component extracted in step S1 is expressed as:
in the method, in the process of the invention,Nrepresenting the length of the signal.
Dynamic pressure of shock wave flow fieldMThe component matrix obtained by extracting the repeated measurement result is as follows:
will beC R The rewritten as a set of column vectors is:
in the method, in the process of the invention,
。
each column of data in the component matrix using self-service method
Making an equiprobable put back resamplingMObtaining self-service sample vectorY b The method comprises the following steps:
in the method, in the process of the invention,C b （m) Is a self-help sampleY b The first of (3)mData.
Calculating self-service samplesY b The average value of (2) is:
for a pair ofY n Repeated self-help sampling processBNext, obtainBThe self-service samples are:
because the value of B is very large, the obtained large sample mean value sequence is as follows:
to obtainY n The optimal estimation value of (2) is obtained by sequencing and segmenting the large sample mean value sequence by adopting a statistical histogram methodY n The optimal estimate of (2) is:
in the method, in the process of the invention,Qgrouping the statistical histogram;c q andf q respectively the firstqMedian and probability of group data.
Further, aiming at the trend component, the ringing component, the low-frequency noise component and the high-frequency noise component after self-service resampling, according to the characteristic that repeated measurement data at any moment after the resampling is subjected to normal distribution, based on the conjugate prior Bayesian theory, the reliable evaluation of the time-varying uncertainty of each component is realized, and the dynamic pressure measurement uncertainty evaluation result of the shock wave flow field is obtained through synthesis. The uncertainty evaluation result not only characterizes the repeatability of shock dynamic pressure measurement, but also contains the interactive relation between the data of adjacent moments of the measurement signals, and has innovation in the field of time-varying uncertainty evaluation. The specific process is as follows.
The large sample data obtained by the steps obeys normal distribution
To obtain the productnThe statistics of time are:
in the method, in the process of the invention,
and->
Independent of each other and satisfy->
And->
。
obtaining
The joint prior probability density function of (2) is:
in the same way, the processing method comprises the steps of,nthe statistics of the data at time +1 are:
constructionnThe likelihood function of the data at time +1 is:
according to a Bayes formula, calculating a joint posterior probability density function as follows:
in the method, in the process of the invention,
；/>
。
obtaining
Posterior distribution compliance->
And->
Wherein
，/>
。/>
Is the mathematical expectation or mean value of normal distribution, sigma 2 The variance represents the degree of dispersion of the data.
Sigma is derived from the definition of the inverse gamma distribution 2 The mathematical expectation of (a) is:
in the method, in the process of the invention,
，/>
。
dynamic pressure measurement result of shock wave flow fieldnThe standard uncertainty of the data at time +1 is:
evaluating uncertainty of data at any time of the trend component, the low frequency noise component, the ringing component and the high frequency noise component according to formula (24), to obtain uncertainty of four components as
Whereint 0 =1/f s ，f s The data sampling frequency is measured for the dynamic pressure of the shock wave flow field.
The expansion uncertainty of dynamic pressure measurement of the shock wave flow field is as follows:
in the method, in the process of the invention,
、/>
、/>
and->
Measurement uncertainty of the trend component, the ringing component, the low-frequency noise component and the high-frequency noise component respectively;kin order for the spreading factor to be a factor,kthe value of (2) is 2-3, and is generally obtained empiricallyk=2。
The invention embodiment shock wave flow field dynamic pressure measurement uncertainty evaluation system is mainly used for realizing the method embodiment, and the system comprises:
the signal decomposition module is used for decomposing the dynamic pressure measurement signal of the shock wave flow field to obtain four components: a high frequency noise component, a trend component, a ringing component, and a low frequency noise component;
the sample size expansion module is used for respectively carrying out sample size expansion on the four extracted components and calculating the optimal estimated value of the data of each component at each moment;
the standard uncertainty calculation module is used for calculating the statistical mean value, the variance and the normal distribution of the optimal estimation value sequence of each component, estimating a probability density function according to the conjugated prior distribution rule, further obtaining a joint prior probability density function of data at each moment, obtaining a joint posterior probability density function and posterior distribution statistic based on a likelihood function and a Bayesian method, and further obtaining the uncertainty of each component;
and the signal uncertainty calculation module is used for carrying out synthesis calculation on the uncertainties of the four components to obtain the expansion uncertainty of the dynamic pressure measurement of the shock wave flow field.
The signal decomposition module is specifically used for decomposing the dynamic pressure measurement signal of the shock wave flow field by utilizing variation modal decomposition to obtain a series of narrowband eigenmode functions, and extracting the narrowband eigenmode functions with the center frequency higher than the ringing frequency to obtain a high-frequency noise component; reconstructing the rest narrow-band eigenmode functions, decomposing the reconstructed signals into a plurality of local oscillation mode functions by using empirical mode decomposition, and decomposing the local oscillation mode functions into a trend component, a ringing component and a low-frequency noise component; wherein the trend component is the eigenmode function with the lowest frequency; the eigenmode function of the ringing energy loss rate smaller than a certain threshold is the ringing component, otherwise is the low-frequency noise component.
Further, the sample size expansion module specifically adopts a self-service resampling method to expand the sample size of the four extracted components.
Further, the sample size expansion module is specifically used for repeatedly measuring the dynamic pressure of the shock wave flow field for M times, extracting to obtain a component matrix, and rewriting the component matrix into a form of a group of column vectors; the self-help method is adopted to carry out equal probability on each column of vectors in the component matrix, resampling can be carried out for a plurality of times, self-help sample vectors are obtained, and the average value of the self-help sample vectors is calculated; repeating the self-help sampling process for a plurality of times on the self-help sample vector to obtain a plurality of self-help samples, and calculating a large sample mean value sequence; and sequencing and segmenting the large sample mean value sequence by adopting a statistical histogram method, and calculating an optimal estimated value.
The present application also provides a computer readable storage medium, such as a flash memory, a hard disk, a multimedia card, a card memory (e.g., SD or DX memory, etc.), a Random Access Memory (RAM), a Static Random Access Memory (SRAM), a read-only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), a programmable read-only memory (PROM), a magnetic memory, a magnetic disk, an optical disk, a server, an App application store, etc., having stored thereon a computer program that when executed by a processor performs a corresponding function. The computer readable storage medium of the present embodiment is for implementing the shock flow field dynamic pressure measurement uncertainty assessment method of the method embodiment when executed by a processor.
The measuring method comprises the steps of measuring and analyzing a dynamic pressure signal of a shock wave flow field generated by a shock wave pipe system by using a KISTLER 7031 piezoelectric pressure sensor, wherein the sampling frequency of data is 5MHz, the flow field medium is air, and the uncertainty of repeated measurement data of the dynamic pressure is evaluated by adopting the embodiment of the method:
1. the dynamic pressure of the shock wave flow field is measured for 5 times repeatedly, as shown in figure 2;
2. extracting multiple components from each shock tube flow field dynamic pressure measurement data in fig. 2 to obtain four component extraction results, including a trend component, a low noise component, a ringing component and a high frequency noise component, as shown in fig. 3 (a) -3 (e);
3. performing sample size expansion on the multi-component extracted signal of the repeated measurement signal;
4. calculating the optimal estimated mean and standard uncertainty of the four component signals of FIGS. 3 (a) -3 (e), see FIG. 4, and calculating the mean and standard uncertainty in the spreading factor according to the uncertainty synthesis method of equation (25)kShock flow field dynamic pressure measurement uncertainty at=2, see fig. 5. Therefore, the uncertainty assessment method for dynamic pressure measurement of the shock wave flow field is suitable for repeated measurement data with small sample size and time-varying measurement data, compared with the traditional method, the uncertainty assessed by the method not only comprises the dispersibility among repeated measurement data at a single moment, but also fully considers the interaction among the data at adjacent moments of a dynamic measurement signal, and compared with the traditional GUM method, the uncertainty of dynamic measurement can be assessed more reliably.
In summary, the embodiment of the invention allows the shock wave flow field dynamic pressure measurement data to have small sample size and high data change frequency, and can fully utilize the relation between the adjacent moment data of the time-varying measurement result to realize the uncertainty assessment of the shock wave flow field dynamic pressure measurement with small sample time-varying characteristics.
It will be understood that modifications and variations will be apparent to those skilled in the art from the foregoing description, and it is intended that all such modifications and variations be included within the scope of the following claims.
Claims (10)
1. The method for evaluating the uncertainty of dynamic pressure measurement of the shock wave flow field is characterized by comprising the following steps of:
s1, decomposing a dynamic pressure measurement signal of a shock wave flow field to obtain four components: a high frequency noise component, a trend component, a ringing component, and a low frequency noise component; wherein the high-frequency noise component is a narrow-band eigenmode function with a center frequency higher than the ringing frequency; the trend component is an eigenmode function with the lowest frequency; the eigenmode function of the ringing energy loss rate smaller than a certain threshold value is a ringing component, otherwise, the eigenmode function is a low-frequency noise component;
s2, respectively expanding sample size of the extracted four components, and calculating an optimal estimated value of each component at each moment of data;
s3, calculating a statistical mean value, a statistical variance and normal distribution of the optimal estimation value sequence of each component, estimating a probability density function according to a conjugated prior distribution rule, further obtaining a joint prior probability density function of data at each moment, and obtaining a joint posterior probability density function and posterior distribution statistics based on a likelihood function and a Bayesian method, further obtaining uncertainty of each component;
and S4, synthesizing and calculating the uncertainty of the four components to obtain the dynamic pressure measurement expansion uncertainty of the shock wave flow field.
2. The method of claim 1, wherein step S1 comprises the steps of:
s11, decomposing a dynamic pressure measurement signal of the shock wave flow field by utilizing variation modal decomposition to obtain a series of narrow-band eigenmode functions, and extracting the narrow-band eigenmode functions with the center frequency higher than the ringing frequency to obtain a high-frequency noise component;
s12, reconstructing the rest narrow-band eigenmode functions, decomposing the reconstructed signals into a plurality of local oscillation mode functions by using empirical mode decomposition, and decomposing the local oscillation mode functions into a trend component, a ringing component and a low-frequency noise component.
3. The method for evaluating uncertainty of dynamic pressure measurement of shock wave flow field as set forth in claim 1, wherein in step S2, a self-service resampling method is specifically adopted to expand sample size of the four extracted components.
4. The method for evaluating uncertainty of dynamic pressure measurement of shock wave flow field according to claim 1, wherein step S4 is specifically to calculate the arithmetic square root of uncertainty of four components, and multiply the arithmetic square root with an expansion coefficient to obtain the expansion uncertainty of dynamic pressure measurement of shock wave flow field.
5. The method for evaluating uncertainty of dynamic pressure measurement of shock wave flow field according to claim 1, wherein step S2 specifically comprises:
s21, repeatedly measuring dynamic pressure of the shock wave flow field for M times, extracting to obtain a component matrix, and rewriting the component matrix into a form of a group of column vectors;
s22, carrying out equal probability on each column of vectors in the component matrix by adopting a self-help method, and resampling for a plurality of times to obtain self-help sample vectors, and calculating the average value of the self-help sample vectors;
s23, repeating the self-help sampling process for the self-help sample vector for a plurality of times to obtain a plurality of self-help samples, and calculating a large sample mean value sequence;
s24, sequencing and segmenting the large sample mean value sequence by adopting a statistical histogram method, and calculating an optimal estimated value.
6. A shock flow field dynamic pressure measurement uncertainty assessment system, comprising:
the signal decomposition module is used for decomposing the dynamic pressure measurement signal of the shock wave flow field to obtain four components: a high frequency noise component, a trend component, a ringing component, and a low frequency noise component; wherein the high-frequency noise component is a narrow-band eigenmode function with a center frequency higher than the ringing frequency; the trend component is an eigenmode function with the lowest frequency; the eigenmode function of the ringing energy loss rate smaller than a certain threshold value is a ringing component, otherwise, the eigenmode function is a low-frequency noise component;
the sample size expansion module is used for respectively carrying out sample size expansion on the four extracted components and calculating the optimal estimated value of the data of each component at each moment;
the standard uncertainty calculation module is used for calculating the statistical mean value, the variance and the normal distribution of the optimal estimation value sequence of each component, estimating a probability density function according to the conjugated prior distribution rule, further obtaining a joint prior probability density function of data at each moment, obtaining a joint posterior probability density function and posterior distribution statistic based on a likelihood function and a Bayesian method, and further obtaining the uncertainty of each component;
and the signal uncertainty calculation module is used for carrying out synthesis calculation on the uncertainties of the four components to obtain the expansion uncertainty of the dynamic pressure measurement of the shock wave flow field.
7. The system for assessing uncertainty in dynamic pressure measurement of a shock wave flow field according to claim 6, wherein the signal decomposition module is specifically configured to decompose the dynamic pressure measurement signal of the shock wave flow field by using variation mode decomposition to obtain a series of narrowband eigenmode functions, and extract the narrowband eigenmode functions with a center frequency higher than a ringing frequency to obtain a high-frequency noise component; and reconstructing the rest narrow-band eigenmode functions, decomposing the reconstructed signals into a plurality of local oscillation mode functions by using empirical mode decomposition, and decomposing the local oscillation mode functions into a trend component, a ringing component and a low-frequency noise component.
8. The shock wave flow field dynamic pressure measurement uncertainty evaluation system of claim 6, wherein the sample size expansion module specifically adopts a self-service resampling method to expand the sample size of the extracted four components.
9. The system for assessing uncertainty in dynamic pressure measurement of a shock wave flow field according to claim 6, wherein the sample size expansion module is specifically configured to perform M repeated measurements on dynamic pressure of the shock wave flow field, extract a component matrix, and rewrite the component matrix into a form of a set of column vectors; the self-help method is adopted to carry out equal probability on each column of vectors in the component matrix, resampling can be carried out for a plurality of times, self-help sample vectors are obtained, and the average value of the self-help sample vectors is calculated; repeating the self-help sampling process for a plurality of times on the self-help sample vector to obtain a plurality of self-help samples, and calculating a large sample mean value sequence; and sequencing and segmenting the large sample mean value sequence by adopting a statistical histogram method, and calculating an optimal estimated value.
10. A computer storage medium having stored therein a computer program executable by a processor for performing the shock flow field dynamic pressure measurement uncertainty assessment method of any one of claims 1-5.
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