CN-121984509-A - Compressed sampling system and reconstruction method suitable for high dynamic range broadband signal

CN121984509ACN 121984509 ACN121984509 ACN 121984509ACN-121984509-A

Abstract

A compression sampling system and a quick reconstruction method suitable for high dynamic range broadband signals are provided, the method is used for processing blade tip vibration monitoring signals of an aeroengine, and in the method, hardware parameters of a modulation broadband converter MWC and a threshold value of a self-recovery analog-to-digital converter SR-ADC are set on the basis of a signal Nyquist rate f NYQ , a bandwidth B, an effective frequency band number K and a maximum amplitude A max a priori; the method comprises the steps of carrying out multichannel frequency band demodulation, low-pass filtering and analog-to-digital sampling on signals by using a modulation broadband converter and a double-threshold self-recovery analog-to-digital converter to obtain output of each channel, recovering correct amplitude information from the acquired signals according to double-threshold information, constructing continuous signals to a finite field conversion module, adaptively solving a frequency spectrum support set by using a variable decibel leaf inference, energy aggregation, FDR significance detection and BIC model reduction algorithm, carrying out up-sampling and frequency band modulation on a low-rate sample sequence based on the frequency spectrum support set, and reconstructing a high dynamic range time domain signal meeting Nyquist rate and a complete frequency spectrum located in an original frequency band.

Inventors

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

Assignees

西安交通大学

Dates

Publication Date: 20260505
Application Date: 20251231

Claims (10)

1. A reconstruction method suitable for compressed sampling of high dynamic range broadband signals, the method being used for processing of aircraft engine tip vibration monitoring signals, the method comprising the steps of: Step S1, hardware parameters of a modulation wideband converter MWC and a threshold value of a self-recovery analog-to-digital converter SR-ADC are set a priori based on a signal Nyquist rate f NYQ , a bandwidth B, an effective frequency band number K and a maximum amplitude A max ; S2, carrying out multi-channel frequency band demodulation, low-pass filtering and analog-to-digital sampling on signals by using a modulation broadband converter architecture and a double-threshold self-recovery analog-to-digital converter to obtain the output of each channel; s3, recovering correct amplitude information from the acquired signals according to the double-threshold information, and constructing continuous signals to a finite field conversion module; S4, utilizing a variable decibel leaf-based inference, energy aggregation, FDR significance detection and BIC model reduction algorithm to adaptively solve a spectrum support set; And S5, up-sampling and frequency band modulating the low-rate sample sequence based on the frequency spectrum support set, and reconstructing a high dynamic range time domain signal meeting the Nyquist rate and a complete frequency spectrum positioned in an original frequency band.
2. A method for reconstructing a compressed sample of a signal according to claim 1, wherein step S1 comprises: The hardware parameters include a mixed waveform parameter, a low-pass filter cut-off frequency f c , a single-channel sampling rate f s and a sampling channel number M, the mixed waveform parameter comprises a period T p and a segmentation number M, the threshold values comprise a threshold value lambda 1 and a threshold value lambda 2 respectively representing the 1 st and the 2 nd SR-ADCs, the signal amplitude ranges which can be acquired are [ -lambda 1 ,λ1 1 ] and [ -lambda 2 ,λ 2 ], Mixing waveform p i (T), i=1, 2,..m is a periodic signal of T p , wherein f p ＝1/T p is greater than or equal to B and determines the upper limit of T p , so that all slices are not overlapped when the frequency band is moved, and the segmentation number M is as follows The mixing waveform selects a pseudo-random sequence consisting of + -1, the expression of which is: The mixed signal is sampled after low-pass filtering, the cut-off frequency and the sampling rate of the filter meet the Nyquist condition, f c ≤f s /2, and sampling aliasing is avoided, and the single-channel sampling rate f s is not less than the frequency f p of the mixed waveform p i (t); The signals y 1 (t) and y 2 (t) collected by the two self-recovery analog-to-digital converters SR-ADC are the remainder of original signals after modulo operations by lambda 1 and lambda 2 respectively, and the following relation is satisfied: Wherein x (t) represents an original signal, y 1 (t) and y 2 (t) represent signals acquired by the 1 st and 2 nd self-recovery analog-to-digital converters SR-ADC respectively; Representing the fractional part of a certain number, the thresholds lambda 1 and lambda 2 meet the integral multiple of a certain positive number gamma, lambda 1 ＝Γl 1 /2,λ 2 ＝Γl 2 /2,l 1 and l 2 are positive integers, and the two meet the mutual quality relation, the maximum amplitude A max of the signal to be measured does not exceed half of the generalized least common multiple of lambda 1 and lambda 2 , A max ≤Γl 1 l 2 /2 (3) Wherein Γl 1 l 2 is the generalized least common multiple of the threshold lambda 1 and the threshold lambda 2 .
3. A method for reconstructing a compressed sample of a signal according to claim 2, wherein step S2 comprises: In the i-th channel, i=1, 2,..m, the mixing signal p i (T) is a signal with a period of T p , and fourier-spread: Wherein P i (f) represents the spectrum of the ith channel mixing signal P i (t), Representing the unit imaginary number, e representing the Euler constant, c il corresponding to the Fourier expansion coefficient, multiplying the original signal x (t) with the mixed signal p i (t) in the time domain to obtain the baseband shifting signal And obtain a frequency domain representation thereof: Wherein x represents a convolution mathematical operation, Shifting baseband signals Input to a low-pass filter, the time domain impulse response of the filter is h (t), the corresponding output y i (t) has the expression in the frequency domain: Where H (f) is the frequency domain response function of the low pass filter, Inputting the low-pass filtered time domain continuous signal y i (t) into a self-recovery analog-to-digital converter SR-ADC, and obtaining a mode sample as And Wherein the method comprises the steps of And The nth output values of the SR-ADC, respectively representing the threshold lambda 1 and the threshold lambda 2 in the ith channel of the modulated wideband converter MWC, N being an integer taken from 0 to N-1, N representing the sample length of the output.
4. A method for reconstructing a compressed sample of a signal according to claim 3, wherein in step 3: The data acquired by the ith channel in the modulated wideband converter MWC calculate the nth sample difference q n obtained by the dual-threshold co-sampling of the ith channel: Let the peak-to-peak values of the two-way self-recovering analog-to-digital converter SR-ADC be delta 1 ＝2λ 1 and delta 2 ＝2λ 2 , respectively, and calculate the difference sigma between the two, sigma=delta 2 -Δ 1 , If |q n |≤σ(Δ 1 /(2σ) +0.5), then the folded integer u n,2 of the SR-ADC with threshold value λ 2 is: u n,2 ＝round(q n /σ) (10) Otherwise, the folded integer u n,2 of the SR-ADC with the threshold value lambda 2 is: u n,2 ＝-sign(qn)·round((Δ 1 -|q n |)/σ) (11) wherein round (·) represents a rounding operation, sign (·) represents a sign function, the value of which is equal to 1 or-1, Then the folded integer u n,1 of the self-recovering analog-to-digital converter SR-ADC with threshold lambda 1 is calculated: u n,1 ＝round((u n,2 Δ 2 -q n )/Δ 1 ) (12) finally, reconstructing the correct amplitude y i [ n ] of the nth sample acquired by the ith channel: analyzing samples obtained by collaborative sampling of double thresholds of all channels respectively to obtain samples with correct amplitude values: y 1 [n],y 2 [n],…,y m [n],n=0,1,...,N-1, performing discrete time fourier transform on the sampling sequence y i [ n ]: Wherein: f s is the sampling frequency of the SR-ADC, L 0 is a non-negative integer of the maximum shift order to be calculated after the characteristic signal spectrum is subjected to periodic mixing after being sampled by the SR-ADC of the self-recovery analog-to-digital converter, and the value is In order to round up the operator, And (3) converting the rewritten formula (14) into a matrix format to obtain: Let the first term on the right of the equation be a and the second term be z (f), l=2l 0 +1 represents the number of shift orders for all to be involved, resulting in y (f) =az (f), where Representing the complex number of the field of the data, Constructing a CTF module, and converting the IMV problem into a multi-measurement vector problem: Constructing a covariance matrix Q of the sampling sequence y [ n ] taking into account all m channels of the modulation wideband converter MWC, and then performing characteristic decomposition on Q to obtain Q=VV H , wherein H (·) represents conjugate transposition operation, thereby constructing a new equation: V=AU+E (16) Wherein: The equivalent observed value matrix is obtained after the covariance matrix Q characteristic constructed by the sampling sequence y [ n ] is decomposed, and P is the column number of the V matrix, namely the number of equivalent observed values, also called snapshot number; Is an equivalent sparse representation coefficient matrix, the support set to be solved Support set formed by z (f) The same is true of the fact that, To measure noise, the transition from the IMV problem of equation (15) to the MMV problem of equation (16) is completed.
5. The method for reconstructing a compressed sample of a signal as recited in claim 4, wherein step S4 comprises: V=au+e, equation (16) is an MMV problem with the objective to recover P sparse representation coefficient vectors U of length L from P noisy measurement vectors V of length m, where the vectors U (p) of length L, p=1, 2..p sets have the same support set, i.e. joint sparsity, in bayesian sparse modeling U has a second order level priors, for the first layer U is modeled as a gaussian distribution controlled by the parameter a, i.e.: Wherein: A non-negative hyper-parameter vector for controlling the sparsity of the matrix U, U l,: representing the first row of the matrix U, p (·) representing the probability density function; indicating u l,: obeys a mean of 0 and a variance of The second layer of a priori modeling is about the hyper-parameters { alpha l } obeying a Gamma distribution with shape parameters a and scale parameters b, namely: Wherein: Representing Gamma function, Γ -1 (·) represents taking the reciprocal of the calculation result of Γ (·) function, modeling the measurement noise matrix E as complex Gaussian distribution with zero mean and covariance Gamma -1 I P , and the hyper-parameter Gamma obeys Gamma distribution with shape parameter c and scale parameter d: p(γ)=Gamma(γ|c,d)=Γ -1 (c)d c γ c-1 e -dγ (19-b) According to the theory of variational Bayesian inference, provision is made for For the hidden variables of the level prior, and in combination with the mean field assumption, the variational distribution is expressed as q (θ) =q u (U)q α (α)q γ (γ), the objective of variational inference is to find the distribution function q (θ) so that the Kullback-Leibler divergence KL (q||p) between the variational function q (θ) and the true posterior distribution p (θ|v) is sufficiently small, and the minimization of the KL divergence is equivalent to the maximization of the evidence lower bound L (q), and the relationship exists between the variational function q (θ): lnp(V)=L(q)+KL(q||p) (20-a) Wherein ln p (V) is the logarithmic form of the marginal probability density function of the equivalent observed value matrix V, the value of which is irrelevant to theta, L (q) is a strict lower bound of ln p (V) because KL (q p) is more than or equal to 0, Maximizing L (q) requires calculating posterior distribution of hidden variables U, α, and γ, q u (U) is updated according to the nature of gaussian distribution, and posterior mean μ and covariance Φ are: μ=γΦA H V (21-a) Φ=(γA H A+D) -1 (21-b) Wherein: diag {.cndot } is a diagonal matrix operation, and the expansion of equation (20-b) yields: wherein p (V|AU, gamma) is a likelihood function, defining I.I F is the F-norm of the matrix, arbitrary for any given property of the smooth function Constructing the Lipschitz upper bound for f (U): wherein < F > represents the Frobenius inner product operation, < X, Y > F ＝tr(X H Y), tr (·) represents the trace of the matrix, let Substituting original likelihood function and constructing lower bound of relaxation evidence Obtaining: Wherein: Next, q u (U)、q α (α) and q γ (γ) and the auxiliary variable Z are solved separately using a variational expectation maximization algorithm, first step E, for q u (U), and then back-off means And covariance Σ is: for q α (α): for q γ (γ): Wherein: Σ l,l is the element of the first row and first column of the covariance matrix, And secondly, M steps are used for updating the auxiliary variable Z, and the expression is as follows: taking the derivative of the above equation with respect to the auxiliary variable Z and letting it be zero, we get z=μ, Taking T=2λ max (A H A)+10 -10 , wherein λ max (X) represents the maximum eigenvalue of matrix X, and iteratively performing (25) - (28) until Stopping the iterative process to obtain a final estimation matrix Where epsilon represents the iteration convergence threshold, Represents the kth iteration As a result of (a), Estimated value And (3) correcting: First, energy combining, the spectrum of the MWC has conjugate symmetry characteristics, i.e., z (f) =z * (-f),(·) * represents conjugate operation, so indexes L and l+1-L represent two-sided images of the same physical band, defining Is a matrix The energy of the first row is combined with the energy of the conjugate symmetry term, namely E' l ＝E l +E l* , Secondly, performing primary screening on a support set by adopting an FDR control principle, ensuring that the expected value of the overall false detection rate is not greater than a threshold value q, considering zero assumption that H0: E' l comes from pure noise distribution for each frequency slice l, calculating the mean mu and the scale sigma by utilizing a mean+MAD robust estimation criterion, and obtaining a standardized statistic And double-sided p values, p l ＝2Φ(-|z l |), Φ (·) represents a standard normal distribution cumulative function, after calculating the p values, all p values are arranged in ascending order to obtain p (1) ≤p (2) ≤…p (L) , and Benjamini-Hochberg (BH) FDR control is used on all p l , and the largest l is selected to satisfy: where q is the artificially specified false positive rate, the first l most significant indices form a preliminary support set, while this support set still contains weakly correlated or redundant indices, Then, a Bayesian information criterion is introduced to further accurately screen the support set, and the support set screened by FDR control is set as The maximum likelihood estimation residual of the model is: Wherein: Representing a pseudo-inverse operation; representing the screening of the index from the original A matrix as For penalty parameter number, the BIC criterion is used: Where I·| represents the number of elements, each index in the support is tried to be removed one by one according to equation (31), and if BIC decreases, it is stated that the index is not an essential signal component, i.e. the model interpretation effort decreases less than the benefit of the parameter decrease, and then culled to the final support set After the final support set is determined, the solution is directly solved on the support with the normal least squares: Wherein: Is the representation factor on the final support set.
6. The method for reconstructing a compressed sample of a signal according to claim 5, wherein step S5 comprises: for least squares solution Each frequency spectrum component in the spectrum is interpolated to the length corresponding to the Nyquist rate of the original signal through a Fourier interpolation function interpft (. Cndot.), and the signal up-sampling is completed, so that a sequence is obtained H I [ n ] represents the time domain response function of the interpolation filter; initializing zero signals consistent with original signal length Indexing according to its corresponding support set The carrier signal of the frequency band where the frequency spectrum component is located is calculated by the frequency f p corresponding to the non-negative integer L 0 of the maximum shift order and the frequency mixing waveform period And sum the interpolated spectral components at baseband Multiplying and accumulating to finally recover the original Nyquist signal Namely: Wherein: the real part is taken and is subjected to fast Fourier transform to obtain the complete frequency spectrum of the original frequency band.
7. A method of reconstructing a compressed sample of a signal according to claim 1, wherein the threshold λ 1 and the threshold λ 2 satisfy λ1< λ2 and the ratio of them is irrational or reciprocal rational to ensure that the difference in folding times of any real amplitude in two folded samples can be uniquely decoded.
8. A system for performing the method of any one of claims 1-7, comprising: a multi-channel modulated wideband converter comprising a mixer array, a low pass filter bank; a dual-threshold self-recovery analog-to-digital converter array, wherein each channel of the modulation broadband converter is connected with two self-recovery analog-to-digital converters with different quantization thresholds; the amplitude unfolding module is used for fusing the two-way folded samples to recover the real amplitude; the CTF conversion module is used for constructing an MMV sparse model; The Bayesian spectrum reasoning engine integrates variation inference, FDR detection and BIC reduction units; And the signal reconstruction module is used for performing spectrum interpolation, carrier modulation and time domain synthesis.
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 implements the method of any of claims 1-7 when the program is executed.

Description

Compressed sampling system and reconstruction method suitable for high dynamic range broadband signal Technical Field The invention relates to the technical field of aeroengine signal sampling and signal processing, in particular to a compressed sampling system and a rapid reconstruction method suitable for a high dynamic range broadband signal. Background The signal acquisition technology is a foundation stone for digital signal processing, and lays an important foundation for subsequent signal transmission and analysis. The traditional sampling theory with Shannon-Nyquist (Shannon-Nyquist) sampling theorem as a core requires that the Analog-to-Digital Converter (ADC) converter must meet two conditions, (1) the sampling rate is not lower than twice the highest frequency of the signal, and (2) the quantization range must cover the dynamic range of the signal. However, with the widespread use of high frequency, high dynamic range (HIGH DYNAMIC RANGE, HDR) signals in modern communications, radar, and like sensing systems, conventional ADCs face significant challenges in both rate and dynamic range. To reduce the sampling rate, sub-nyquist sampling (compressed sampling) techniques have been developed in which a modulated wideband converter (Modulated Wideband Converter, MWC) acts as a typical wideband sparse signal sampling structure that enables blind sampling and reconstruction of multi-band signals with unknown spectral support, effectively reducing the sampling rate from the nyquist rate to the order of the bandwidth actually occupied by the signal through multi-channel periodic mixing and low-speed sampling. However, the conventional MWC system still has the obvious defect in a high dynamic range signal scene that saturation distortion occurs when the signal amplitude exceeds the quantization range of the ADC, which seriously affects the accuracy of subsequent frequency spectrum and signal recovery. To break through the above limitations, the related industry has proposed Analog-to-digital sampling (also called infinite sampling) techniques that collect a pattern sample of the original amplitude of the signal by a Self-recovery Analog-to-Digital Converter (SR-ADC) and recover the true amplitude from the pattern sample of the signal. However, the mode sampling frequency of the existing HDR signal is much higher than the nyquist rate, and in terms of signal reconstruction, the conventional MWC relies on a greedy algorithm, which relies on a spectrum sparseness priori, and has limited performance and higher computational complexity in a noise environment. Therefore, in order to further reduce the sampling, storage, and post-processing components of the wideband sparse HDR signal, a compressed sampling system and a fast reconstruction method suitable for the wideband signal with a high dynamic range are needed to recover the amplitude and spectrum of the original wideband sparse HDR signal from the compressed sampled pattern sample. 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 compressed sampling system and a rapid reconstruction method suitable for high dynamic range broadband signals, which recover the amplitude of an HDR broadband signal from compressed sampling folded samples with the rate lower than Nyquist, so as to realize stable and efficient spectrum reconstruction and signal reconstruction, and provide a practical compressed sampling scheme for low-power consumption, low-cost and low-bandwidth sampling of the HDR signal. A reconstruction method for compressed sampling of high dynamic range broadband signals for use in the processing of aircraft engine tip vibration monitoring signals, the method comprising: Step S1, hardware parameters of a modulation wideband converter MWC and a threshold value of a self-recovery analog-to-digital converter SR-ADC are set a priori based on a signal Nyquist rate f NYQ, a bandwidth B, an effective frequency band number K and a maximum amplitude A max; S2, carrying out multi-channel frequency band demodulation, low-pass filtering and analog-to-digital sampling on signals by using a modulation broadband converter architecture and a double-threshold self-recovery analog-to-digital converter to obtain the output of each channel; s3, recovering correct amplitude information from the acquired signals according to the double-threshold information, and constructing continuous signals to a finite field conversion module; S4, utilizing a variable decibel leaf-based inference, energy aggregation, FDR significance detection and BIC model reduction algorithm to adaptively solve a spectrum support set; And S5, up-sampling and frequency band modulating the low-rate sample sequence based on t