A time-varying bandpass filtering method under linear frequency modulation excitation

Abstract

This invention belongs to the field of signal processing technology, specifically relating to a time-varying bandpass filtering method under linear frequency modulation (LFM) excitation. In the process of measuring the dynamic fluid level in an oil well, an LFM signal is sent to excite the air column inside the pipe. The acoustic signal after excitation is collected and processed. The fluid level depth is measured based on the mathematical relationship between the extracted resonance characteristics and the pipe length. The processing of the sensor signal obtained through continuous resonance of the LFM acoustic wave includes: discretely sampling the sensor signal to obtain the target signal; constructing an inverse slope LFM signal and multiplying it with the target signal to obtain an approximate steady-state signal; filtering the approximate steady-state signal using a bandpass filter to obtain a bandpass-filtered steady-state signal; and multiplying the bandpass-filtered steady-state signal with the complex conjugate signal of the inverse slope LFM signal to recover the LFM excitation and its response. This invention has advantages such as low computational load in the filtering process and low filtering delay.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a time-varying bandpass filtering method under linear frequency modulation excitation. Background Technology

[0002] Linear frequency modulated (LFM) signals, whose frequency varies linearly with time, are widely used as excitation signals in radar ranging, oil well dynamic fluid level detection, pipeline blockage location, electromagnetic detection, and fiber optic sensing due to their advantages such as ultra-widebandwidth, large time-delay-bandwidth product, and ease of generation. In practical applications, an LFM signal is generated and emitted by an excitation source, propagates in the target environment, and interacts with the target or medium. The echo signal or specific response carrying target information is then collected by a receiving device. Signal processing algorithms extract feature information and key parameters, thereby calculating parameters such as target distance and medium characteristics to achieve engineering tasks such as distance measurement, target location, and imaging recognition. However, due to the influence of complex background noise in the environment, non-ideal characteristics of the transmission channel, nonlinear response of the transceiver equipment, and resonance effect of the excitation source, the received echo signal often contains noise and high-order response interference, easily drowning out the useful signal and severely affecting the extraction and identification analysis of target information, leading to detection errors or even mission failure. Therefore, before processing the collected signal using algorithms, filtering preprocessing is required to improve the signal's analyzability and anti-interference capability.

[0003] For linear frequency modulation (LFM) excitation, time-varying bandpass filters are commonly used. However, due to the time-varying frequency characteristics of LFM signals, the center frequency of the time-varying bandpass filter needs to follow the instantaneous frequency changes of the LFM signal in real time to scan the entire excitation band. Each time the frequency changes, the filtering process is equivalent to reconstructing a new time-varying bandpass filter. Therefore, when the bandwidth is set large, the filtering process generates a significant computational load, leading to a substantial increase in filtering delay, reduced feature extraction accuracy and precision, and consequently affecting the reliability of the detection results. Summary of the Invention

[0004] To improve the reliability of linear frequency modulated (LFM) excitation filtering during oil well dynamic fluid level measurement, this invention proposes a time-varying bandpass filtering method under LFM excitation. During oil well dynamic fluid level measurement, an LFM signal is sent to excite the air column inside the tubing. The excited acoustic signal is collected and processed. The fluid level depth is measured based on the mathematical relationship between the extracted resonance characteristics and the tubing length. The processing of the sensor signal obtained through continuous resonance of the LFM acoustic wave includes the following steps:

[0005] S1. Acquire the sensing signal and obtain the target signal through discrete sampling;

[0006] S2. Construct a linear frequency modulated signal with an inverse slope and multiply it with the target signal to obtain an approximate steady-state signal;

[0007] S3. Use a bandpass filter to filter the approximate steady-state signal to obtain the bandpass filtered steady-state signal;

[0008] S4. Multiply the steady-state signal after bandpass filtering with the complex conjugate signal of the inverse slope linear frequency modulation signal to recover the linear frequency modulation excitation and its response.

[0009] Furthermore, the target signal f(n) obtained by discrete sampling includes:

[0010] f(n) = f0(n) + f1(n) + r(n);

[0011] Where f0(n) is the linear frequency modulation excitation and its response, expressed as:

[0012]

[0013] f1(n) represents the higher-order linear frequency modulated excitation and its response, expressed as:

[0014]

[0015] Where r(n) is the noise originating from the measurement system and the environment; A is the amplitude; e is the natural constant; j is the imaginary unit; f s denoted as sampling frequency; n as sampling sequence; f0 as initial frequency; k as modulation slope; φ as initial phase; p(n) as response of linear frequency modulation excitation; m as order of higher-order response; q(n) as response of higher-order linear frequency modulation excitation.

[0016] Furthermore, the formula for the constructed inverse slope linear frequency modulated signal g(n) is:

[0017]

[0018] in, This indicates the frequency adjustment.

[0019] Furthermore, the formula for calculating the approximate steady-state signal h(n) is:

[0020]

[0021] Furthermore, the formula for the steady-state signal z(n) after bandpass filtering is:

[0022]

[0023] in, This indicates in-band noise.

[0024] Furthermore, the complex conjugate signal of g(n) The calculation formula is:

[0025]

[0026] Furthermore, the recovered linear frequency modulation excitation and its response c(n) are expressed as follows:

[0027]

[0028] Preferably, the sampling frequency f s Set to 1000Hz.

[0029] Preferably, the slope is set to 3Hz / s.

[0030] Preferably, the bandpass filter used when filtering the near steady-state signal has a center frequency of 20Hz and a bandwidth of 5Hz.

[0031] The beneficial effects of this invention are:

[0032] This invention constructs a linear frequency modulated (LFM) signal with opposite modulation slopes and inverse instantaneous frequency changes, transforming the target LFM signal into an approximately steady-state signal. Interference components are filtered out using a conventional bandpass filter, avoiding the overall excitation band scanning process required by traditional time-varying bandpass filters. This significantly reduces the computational load and filtering time, effectively suppressing interference while preserving the characteristics of the LFM excitation and its response relatively completely, providing a high-quality analyzable signal for subsequent algorithm processing and feature extraction. Attached Figure Description

[0033] Figure 1 This is a flowchart of the method of the present invention;

[0034] Figure 2 This is a time-domain diagram of the target linear frequency modulated signal in the embodiment;

[0035] Figure 3 This is the frequency domain diagram of the target linear frequency modulated signal in the embodiment;

[0036] Figure 4 This is the time-frequency diagram of the target linear frequency modulated signal in the embodiment;

[0037] Figure 5 The time-frequency diagram of the approximate steady-state signal obtained by multiplying the target linear frequency modulated signal and the inverse slope linear frequency modulated signal in the embodiment is shown.

[0038] Figure 6 The above is a time-frequency diagram of the recovered linear frequency modulated signal obtained by multiplying the approximate steady-state signal after bandpass filtering with the complex conjugate signal of the linear frequency modulated signal with inverse modulation slope.

[0039] Figure 7 The above is a time-domain diagram of the recovered linear frequency modulation excitation and its response from the example.

[0040] Figure 8 The above is a frequency domain diagram of the recovered linear frequency modulation excitation and its response from the example. Detailed Implementation

[0041] 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 some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] This invention proposes a time-varying bandpass filtering method under linear frequency modulation excitation. In the process of measuring the dynamic fluid level in an oil well, a linear frequency modulation signal is sent to excite the air column inside the pipe. The acoustic signal after excitation is collected and processed. The fluid level depth is measured based on the mathematical relationship between the extracted resonance characteristics and the pipe length. The processing of the sensor signal obtained through continuous resonance of the linear frequency modulation sound wave includes the following steps:

[0043] S1. Acquire the sensing signal and obtain the target signal through discrete sampling;

[0044] S2. Construct a linear frequency modulated signal with an inverse slope and multiply it with the target signal to obtain an approximate steady-state signal;

[0045] S3. Use a bandpass filter to filter the approximate steady-state signal to obtain the bandpass filtered steady-state signal;

[0046] S4. Multiply the steady-state signal after bandpass filtering with the complex conjugate signal of the inverse slope linear frequency modulation signal to recover the linear frequency modulation excitation and its response.

[0047] Oil well dynamic fluid level measurement is an important application scenario for linear frequency modulated (LFM) excitation methods. This involves sending a LFM signal to excite the air column inside the tubing, collecting the excited acoustic signal, processing it, and then measuring the fluid level depth based on the mathematical relationship between the extracted resonance characteristics and the tubing length. In this embodiment, the collected tubing acoustic signal obtained through continuous resonance of the LFM sound wave is filtered using a time-varying bandpass filtering method under LFM excitation mentioned in this invention.

[0048] Install the measuring device; place the excitation sound source at the inlet of the experimental pipe, and install the sound sensor at the front end of the excitation sound source. Set the signal sampling frequency f. s =1000Hz, total sampling time T=10s, linear frequency modulation excitation starting frequency f L=10Hz, termination frequency f U =40Hz, tuning slope k=3Hz / s.

[0049] like Figure 1 The target signal is obtained by discrete sampling of the acquired sensor signal. The target signal is then multiplied by the inverse slope linear frequency modulated signal to obtain an approximate steady-state signal. This approximate steady-state signal is then filtered using a bandpass filter. Finally, the bandpass-filtered steady-state signal is multiplied by the complex conjugate signal of the inverse slope linear frequency modulated signal to obtain the recovered linear frequency modulated excitation and its response. The following embodiments will describe the above steps in detail.

[0050] Acoustic signals obtained under continuous excitation by linear frequency modulated sound waves are acquired, and the time-domain graph of the target signal f(n) is obtained by discrete sampling, as shown in the figure. Figure 2 As shown, the useful signals that reflect the resonance characteristics are completely drowned out. Figure 3 By extracting the frequency domain signal diagram of the acoustic signal in the frequency range of 0 to 100 Hz, it can be seen that there is a lot of interference in the signal spectrum, making it difficult to extract the resonance characteristics.

[0051] The time-frequency graph of f(n) is as follows Figure 4 As shown, the higher-order response, noise interference, and the frequency range of the linear frequency modulated signal largely overlap, making them impossible to suppress directly through conventional filtering. The components of f(n) are expressed as follows:

[0052] f(n) = f0(n) + f1(n) + r(n);

[0053] Where f0(n) is the linear frequency modulation excitation and its response; f1(n) is the higher-order linear frequency modulation excitation and its response; and r(n) is the noise originating from the measurement system and the environment.

[0054] The formula for calculating the linear frequency modulation excitation and its response f0(n) is as follows:

[0055]

[0056] Where A is the amplitude; e is the natural constant; j is the imaginary unit; f s denoted as sampling frequency; n as sampling sequence; f0 as initial frequency; k as modulation slope; φ as initial phase; p(n) as response of linear frequency modulation excitation, with a frequency similar to that of linear frequency modulation excitation.

[0057] The formula for calculating the higher-order linear frequency modulation excitation and its response f1(n) is as follows:

[0058]

[0059] Where m is the order of the higher-order response; q(n) represents the response of the higher-order linear frequency modulation excitation, with a frequency similar to that of the higher-order linear frequency modulation excitation.

[0060] Based on the frequency characteristics of the linear frequency modulated signal, the inverse slope linear frequency modulated signal g(n) is constructed, and the calculation formula is as follows:

[0061]

[0062] in, This indicates frequency adjustment; in this embodiment, it is set to...

[0063] Multiplying the target signal f(n) by the linear frequency modulated signal g(n) with the inverse slope yields the approximate steady-state signal h(n), calculated using the following formula:

[0064]

[0065] The time-frequency plot of the obtained approximate steady-state signal is as follows: Figure 5 As shown, the overall signal amplitude has increased, the frequency has shifted to an approximate steady-state frequency, and the frequency components are clearly separable. For the approximate steady-state signal h(n), the center frequency f is used. c =20Hz, bandwidth is F b The filtered signal z(n) is obtained by filtering with a bandpass filter of 5Hz. The calculation formula is as follows:

[0066]

[0067] in, This indicates in-band noise.

[0068] Construct the complex conjugate signal of the inverse slope linear frequency modulated signal g(n) The calculation formula is:

[0069]

[0070] The filtered result is compared with the complex conjugate signal. Multiplying the results yields the recovered linear frequency modulated excitation and its response c(n), calculated using the following formula:

[0071]

[0072] The time-frequency diagram of the recovered linear frequency modulated signal is as follows: Figure 6 As shown, it can be seen that other interference components have been effectively filtered out, while the linear frequency modulation excitation and its response have been well preserved and recovered.

[0073] To further observe the filtering effect, the time and frequency domain plots of the recovered linear frequency modulated excitation and its response are shown below. Figure 7 , Figure 8As shown, the higher-order excitation and response of the linear frequency modulation signal and its noise interference are effectively suppressed, and the signal exhibits obvious periodicity, which is beneficial for the extraction of the signal resonance characteristics.

[0074] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A time-varying band-pass filtering method under chirp excitation, in the process of measuring the liquid level of oil well, the air column in the pipe is excited by sending a chirp signal, the excited acoustic signal is collected and processed, and the measurement of the liquid level depth is realized according to the mathematical relationship between the extracted resonance characteristics and the length of the pipe column, characterized in that, The processing of the collected sensing signal obtained by the continuous resonance of the linear frequency modulation sound wave comprises the following steps: S1, obtaining a target signal by discretely sampling the sensing signal; S2, constructing an inverse slope linear frequency modulation signal, i.e. where j is the imaginary unit; is a sampling sequence; is a sampling frequency; denotes an adjustment frequency; denotes an adjustment slope; And multiplying the target signal to obtain an approximate steady-state signal, i.e. wherein, target signal obtained as a discrete sample; is a chirp signal with inverse ramping slope; is an amplitude; e is a natural constant; denotes an initial frequency; denotes an adjusted frequency; is an initial phase; is an order of a high order response; is noise originating from the measurement system and the environment; denotes a response to a chirp excitation; denotes a response to a high order chirp excitation; S3, filtering the approximate steady-state signal by using a band-pass filter to obtain a band-pass filtered steady-state signal, the band-pass filtered steady-state signal The formula is: ； wherein represents in-band noise; S4, multiplying the band-pass filtered steady-state signal with the complex conjugate signal of the dechirped linear frequency modulation signal, recovering the linear frequency modulation excitation and its response The formula is: ； wherein, is a complex conjugate signal of the inverse chirp linear frequency modulated signal is represented as .

2. The method of claim 1, wherein, Target signals obtained by discrete sampling comprising: ； wherein is the chirp excitation and its response, denoted as: ； For the linear frequency modulation higher order excitation and its response, it is expressed as: ； wherein, is the noise originating from the measurement system and the environment; is the amplitude; e is the natural constant; j is the imaginary unit; is the sampling frequency; is the sampling sequence; denotes the initial frequency; denotes the chirp rate; is the initial phase; denotes the response to a linear frequency modulation excitation; is the order of the high order response; denotes the response to a linear frequency modulation high order excitation.

3. The method according to any one of claims 1 to 2, characterized in that, Sampling frequency was set to 1000 Hz.

4. The method according to any one of claims 1 to 2, characterized in that, The slope setting is 3Hz / s.

5. The method of claim 1, wherein, The center frequency of the band-pass filter used when filtering the approximate steady-state signal is 20Hz, and the bandwidth is 5Hz.

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