CN-121978400-A - Rapid frequency measurement method based on multiple same-rate undersampling channels

CN121978400ACN 121978400 ACN121978400 ACN 121978400ACN-121978400-A

Abstract

A rapid frequency measurement method based on a plurality of synchronous rate undersampling channels is suitable for signal processing of aeroengine leaf end timing, distributed sensing passive or limited sampling scenes, and comprises the steps of uniformly sampling signals by using L+1 channels with the same sampling period, forming L groups of non-zero and different delay combinations by constructing time delay between adjacent sampling channels, performing discrete Fourier transform on sampling data of each channel, obtaining an absolute value of Fourier transform coefficients to obtain a frequency spectrum, determining position indexes corresponding to frequency peaks, and selecting the first channel Channel and Fourier transform coefficients of the channels are extracted and corresponding complex numbers are extracted, and complex conjugate corresponding to the first channel is multiplied by The complex number corresponding to the channel, calculating the phase angle of the intermediate variable, solving the equivalent aliasing frequency, traversing and analyzing L groups of double-way delay sampling data, obtaining the corresponding equivalent aliasing frequency and equivalent sampling frequency according to the phase angle values of different delays, and reconstructing the real frequency from the equivalent aliasing frequency and the equivalent sampling frequency by using the Chinese remainder theorem algorithm facing real value signals.

Inventors

CAO JIAHUI
Ma Taian
YANG ZHIBO
CHEN XUEFENG
TIAN SHAOHUA
WU SHUMING
QIAO BAIJIE
SUN RUOBIN

Assignees

西安交通大学

Dates

Publication Date: 20260505
Application Date: 20251231

Claims (10)

1. The rapid frequency measurement method based on a plurality of synchronous rate undersampling channels is characterized by being suitable for signal processing of an aeroengine blade end timing, distributed sensing passive or limited sampling scene, and comprises the following steps of: Step S1, uniformly sampling signals by using L+1 paths of channels with the same sampling period, and forming L groups of non-zero and mutually different delay combinations by constructing time delays between adjacent sampling channels; S2, performing discrete Fourier transform on the sampling data of each channel, taking an absolute value of a Fourier transform coefficient, and determining a position index corresponding to a frequency peak; step S3, selecting a first position index according to the position index corresponding to the frequency peak value Fourier transform coefficients of the channel and the l+1 channel are extracted, corresponding complex numbers are extracted, complex conjugate corresponding to the first channel is multiplied by complex number corresponding to the l+1 channel, the phase angle of the intermediate variable is calculated, and equivalent aliasing frequency is solved; step S4, traversing and analyzing L groups of double-way delay sampling data, repeating the steps S2 to S3, and obtaining corresponding equivalent aliasing frequency and equivalent sampling frequency according to phase angle values under different delays; and S5, reconstructing the real frequency from the equivalent aliasing frequency and the equivalent sampling frequency by using a Chinese remainder theorem algorithm facing the real value signal.
2. A fast frequency measurement method based on a plurality of co-rate undersampling channels according to claim 1, characterized in that step S1 preferably comprises: using L+1 sampling frequencies are all The sampling channels of the filter unit uniformly sample signals, and the corresponding sampling periods are all By constructing the time delay between adjacent sampling channels, L groups of non-zero and different delay combinations can be formed, and the first sampling point of the first +1 channel is delayed from the sampling moment of the first sampling point of the L channel Different delay data satisfies Wherein Is an integer of two mutual qualities, and the sampled data vector obtained by the L+1 path sampling channel is recorded as Wherein P represents the vector length, i.e. the length of the recorded data.
3. The method for rapid frequency measurement based on multiple co-rate undersampling channels according to claim 2, wherein step S2 comprises: At the position of The 1 st to the p-th data are selected to be subjected to discrete fourier transform: ; Wherein the method comprises the steps of Is the sampled signal, k and n are the index sequences traversing from 1 to p, Is an imaginary symbol defined as: , Representation pair The kth data after discrete fourier transform, A fourier transform coefficient vector representing the first channel data, And is opposite to Taking absolute value, carrying out the same operation on all sampling channel data, and determining the position index of the spectrum peak value 。
4. The method for rapid frequency measurement based on multiple co-rate undersampling channels as set forth in claim 1, wherein step S3 includes: Index according to the location of the spectral peak Extracting two corresponding Fourier coefficients from the Fourier coefficient vectors of the first channel and the l+1 channel data And Will be Is conjugated to (a) Multiplied by Obtaining an intermediate variable, calculating the phase angle Divided by Obtaining the first equivalent aliasing frequency : ; Wherein the method comprises the steps of Representing the sampling delay between the first channel and the l +1 channel, Represents the conjugate operation of the two-dimensional code, Representing a complex phase angle defined as follows: ; Wherein, the Representing a complex number with a real part a and an imaginary part b.
5. The method for rapid frequency measurement based on multiple co-rate undersampling channels as set forth in claim 4, wherein in step S4: For L groups of two-way delay sampling data, respectively calculating by using a formula (2) to obtain L corresponding equivalent aliasing frequencies , 。
6. The method for rapid frequency measurement based on multiple co-rate undersampling channels as set forth in claim 5, wherein step S5 includes: Generating remainder sets , , Two elements of (a) are expressed as And I.e. ; Then calculate And Regarding modulus Is recorded as the common remainder of And : , Wherein Is that Is the generalized maximum common factor of (a), i.e Is such that Maximum real numbers of pairwise interstitium; representing modulus as Is used for the modular operation of the (c), Calculating the minimum circumference distance And : ; ; Wherein i and l each represent a slave And Wherein z represents a value selected from the group consisting of An integer of any value; for the ith common remainder from the ith delay scheme, Next, an offset common remainder is calculated And : ; Then the following congruence equation set is established, and q is solved by using the Chinese remainder theorem algorithm: ; wherein q is an integer to be solved; representing modulus as Modulo arithmetic; , , On the basis of solving q, according to the equation Determination of Finally by Reconstructing target frequency 。
7. The rapid frequency measurement method based on a plurality of undersampling channels at the same rate according to claim 1, wherein the sampling frequency of the l+1 channels is lower than twice the highest frequency of the signal to be measured, and the sampling frequency is in an undersampled state.
8. A system for performing the method of any one of claims 1-7, comprising: The uniform sampling module uniformly samples signals by using L+1 paths of channels with the same sampling period, and L groups of non-zero and different delay combinations can be formed by constructing time delays between adjacent sampling channels; The discrete Fourier transform module performs discrete Fourier transform on the sampling data of each channel, takes the absolute value frequency spectrum of the Fourier transform coefficient, and determines the position index corresponding to the frequency peak value; the calculation module selects the first according to the position index corresponding to the frequency peak value Fourier transform coefficients of the channel and the l+1 channel are extracted, corresponding complex numbers are extracted, complex conjugate corresponding to the first channel is multiplied by complex numbers of the l+1 channel, the phase angle of the intermediate variable is calculated, the equivalent aliasing frequency is solved, L groups of double-way delay sampling data are traversed and analyzed, and corresponding equivalent aliasing frequency and equivalent sampling frequency are obtained according to phase angle values under different delays; and the reconstruction module is used for reconstructing the real frequency from the equivalent aliasing frequency and the equivalent sampling frequency by using a Chinese remainder theorem algorithm facing the real value signal.
9. A computer storage medium comprising computer instructions which, when run on a computer, cause the computer to perform the method of any of claims 1-7.
10. An electronic device, the electronic device comprising: a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein, The processor, when executing the program, implements the method of any one of claims 1-7.

Description

Rapid frequency measurement method based on multiple same-rate undersampling channels Technical Field The invention relates to the technical field of signal analysis and signal processing of aeroengine blade end timing, distributed sensing passive or limited sampling scenes, in particular to a rapid frequency measurement method based on a plurality of undersampling channels with the same speed. Background Sampling theory is the basis of digital signal processing and the well-known shannon nyquist sampling theorem states that band-limited analog signals can be perfectly reconstructed from discrete data with sampling frequencies not below the nyquist rate, which has the most profound effect on the industrial development of digital signal processing systems. Multi-rate sampling is a technology in digital signal processing, which refers to processing or transmitting signals in a system with a plurality of different sampling rates, and the core goal is to optimize the system performance, reduce the computational complexity or adapt to the requirements of different modules by flexibly adjusting the sampling rate. However, in a specific application, implementing multi-rate sampling requires multiple sampling devices with different processing rates, which places higher demands on hardware. In the case of passive sampling, for example, in the measurement of timing vibration of the blade end of an aeroengine, the implementation of different sampling rates depends on the specific number and layout of the sensors, so that the measurement cost is greatly increased, and the application development of multi-rate sampling under the passive sampling condition is also limited. Delay estimation is a method of estimating the frequency of a signal using the phase change in a certain time delay. The method requires that the delay time is smaller than the Nyquist interval to accurately identify the signal frequency, when the delay time does not meet the Nyquist interval, a series of aliasing frequencies can be generated by changing the delay time between sampling channels, multi-rate sampling is equivalently realized, and the signal frequency can be recovered from the undersampled signals by combining the thought of 'mutual quality' in Chinese remainder determination. However, for a real signal with positive and negative opposite number frequencies, the correspondence of the aliasing frequency in the nyquist interval to the positive and negative opposite number frequency of the real signal is unknown, i.e. there is a "remainder ambiguity". If the Chinese remainder theorem is directly used for solving the problem, unacceptable errors are introduced, so that the application of the traditional Chinese remainder theorem in real signal frequency recovery is hindered. The above information disclosed in the background section is only for enhancement of understanding of the background of the invention and therefore may contain information that does not form the prior art that is already known to a person of ordinary skill in the art. Disclosure of Invention Aiming at the defects, the invention provides a rapid frequency measurement method, a system, a medium and equipment based on a plurality of same-rate undersampling channels, wherein two equivalent sampling frequencies and equivalent aliasing frequencies are obtained based on delayed sampling of a double-channel, a congruence equation set in a product form is constructed aiming at the problem of remainder ambiguity, and finally the congruence equation set is solved by utilizing an improved Chinese remainder theorem to obtain the final signal frequency. A rapid frequency measurement method based on a plurality of co-rate undersampling channels, the method being suitable for signal processing of aeroengine tip timing, distributed sensing passive or limited sampling scenarios, the method comprising: Step S1, uniformly sampling signals by using L+1 paths of channels with the same sampling period, and forming L groups of non-zero and mutually different delay combinations by constructing time delays between adjacent sampling channels; S2, performing discrete Fourier transform on the sampling data of each channel, taking an absolute value of a Fourier transform coefficient, and determining a position index corresponding to a frequency peak; step S3, selecting a first position index according to the position index corresponding to the frequency peak value Fourier transform coefficients of the channel and the l+1 channel are extracted, corresponding complex numbers are extracted, complex conjugate corresponding to the first channel is multiplied by complex number corresponding to the l+1 channel, the phase angle of the intermediate variable is calculated, and equivalent aliasing frequency is solved; step S4, traversing and analyzing L groups of double-way delay sampling data, repeating the steps S2 to S3, and obtaining corresponding equivalent aliasing frequency and equivalent sampling frequen