A method for frequency identification of measurement while drilling signals

Abstract

The present application discloses a method for frequency identification of a measurement while drilling signal, which relates to the technical field of signal processing. The method comprises the following steps: s ( t ) and noise n ( t ) input a high-order bistable stochastic resonance system; transform the damping coefficient, system parameters and system output response in the high-order bistable stochastic resonance system to obtain an equivalent equation; detect the noise intensity D Is it consistent with the signal to be tested? s ( t ) matches, if it matches, the signal is output directly and the signal to be tested is restored s ( t If the frequency does not match, the parameters of the high-order bistable stochastic resonance system are adjusted according to the parameter adjustment rules. This application solves the problem that the useful signal may be damaged or even unrecognizable during filtering.

Description

Technical Field

[0001] The present application relates to the technical field of signal processing, and in particular to a method for frequency identification of measurement while drilling signals. Background Art

[0002] At present, traditional methods for denoising measurement while drilling signals include FIR (finite impulse response) filtering, wavelet transform, adaptive filtering, median filtering and PCA (principal component analysis).

[0003] The FIR filter detection principle based on frequency domain analysis is relatively simple and can process signals directly in the frequency domain. It is particularly effective for signals with clear and stable frequency components. Furthermore, it can effectively attenuate noise in specific frequency bands when the signal frequency distribution is relatively regular. However, this method performs poorly when processing time-varying, non-stationary signals. Therefore, when applied to weak signal-to-noise ratio signals in complex underground working conditions, useful signals are easily lost.

[0004] Wavelet transform can simultaneously analyze the time-frequency information of a signal and characterize the characteristics of the signal at different times and frequencies. It has a good filtering effect on non-stationary signals and signals with sudden changes. However, this method has the problem that the selection of wavelet basis parameters is difficult and the selection process relies on subjective experience. Different choices will lead to different filtering results.

[0005] Although the stochastic resonance effect generated by a standard high-order bistable system can effectively identify the signal to be measured in a strong noise background, it still has the following drawbacks when applied to measurement while drilling signals:

[0006] ① Due to the limitations of the adiabatic approximation theory, the stochastic resonance effect of the high-order bistable system is only at the frequency of the signal to be measured. f 0 is a small parameter, that is f It occurs when 0 is much smaller than 1. However, when applying the high-order bistable stochastic resonance system to measurement while drilling, the frequency of the measured signal must be preprocessed first;

[0007] ② Although noise plays a positive role in the generation of stochastic resonance effect, if the noise intensity is too large, the system will produce over-resonance, which will cause the resonance output effect to fail. Summary of the Invention

[0008] The purpose of this application is to provide a method for frequency identification of measurement while drilling signals to solve the problem that the application of traditional filtering methods based on noise suppression or cancellation is based on the premise that the measured signal and the noise spectrum do not overlap, which will cause the useful signal to be damaged or even unrecognizable during filtering processing.

[0009] This application adopts the following technical solution: a method for identifying the frequency of a measurement while drilling signal, comprising the following steps:

[0010] The signal to be measured s ( t ) and noise n ( t ) Input the high-order bistable stochastic resonance system and set the conversion coefficient according to the frequency range of the measurement while drilling signal output by the high-order bistable stochastic resonance system R ;

[0011] Transform coefficient R Damping coefficient in high-order bistable stochastic resonance system k , system parameters a 、 b and system output response x By performing transformation, an equivalent equation of a high-order bistable stochastic resonance system is obtained, and the equivalent equation meets the frequency application requirements of the high-order bistable stochastic resonance system;

[0012] Detection noise intensity D Is it consistent with the signal to be tested? s ( t ) matches, if so, restore the signal to be tested s ( t Otherwise, according to the parameter adjustment rules, the parameters of the high-order bistable stochastic resonance system are adjusted to obtain a high-order bistable parameter-adjusted stochastic resonance system, and the high-order bistable parameter-adjusted stochastic resonance system is used to restore the measured signal. s ( t ) frequency.

[0013] In one possible implementation, the high-order bistable stochastic resonance system is expressed as formula (1):

[0014] x" ( t )+ kx' ( t )=-[ dU ( x ( t )) / dx ( t )]+ s ( t )+ n ( t )(1)

[0015] In the above formula, x ( t ) is the output response of the nonlinear system; x' ( t )and x" ( t ) are respectively x ( t )’s first and second derivatives; dU ( x (t )) / dx ( t ) is the nonlinear restoring force; U ( x ( t )) is the potential function, expressed as:

[0016] U ( x ( t ))=- ax 4 ( t ) / 4+ bx 6 ( t ) / 6(2)

[0017] In one possible implementation, the equivalent equation is expressed as formula (3):

[0018] x 1 " ( t )+ k 1 x 1 ' ( t )= a 1 x 1( t ) 3 - b 1 x 1( t ) 5 + A sin(2 πf 0 t + φ )+ n ( t )(3)

[0019] In the above formula, x 1( t ) is the response to the system output x ( t )The result after transformation, x 1 ' ( t )and x 1 " ( t ) are respectively x 1( t ), k 1 is the damping coefficient k The result after transformation, a 1 and b 1 are the system parameters a and b The result after transformation, A 、f 0 and φ The signals to be tested are s ( t )’s amplitude, frequency and initial phase.

[0020] In one possible implementation, the damping coefficient is calculated as follows: k , system parameters a 、 b and system output response x ( t ) to transform:

[0021] k 1= R , a 1= R 6 a , b 1= R 10 b , x 1( t )= x ( t ) / R 2 .

[0022] In one possible implementation, the parameter adjustment rule is:

[0023] When the resonance type is under-resonance, reduce the damping coefficient k , reduce system parameters a Or increase system parameters b ;

[0024] When the resonance type is over-resonance, increase the damping coefficient k , increase system parameters a Or reduce system parameters b .

[0025] The beneficial effects of this application are:

[0026] 1) This application utilizes the dynamic characteristics of high-order bistable nonlinear systems, namely the stochastic resonance effect, to identify sensor signals under strong downhole vibration noise interference. This method not only overcomes the shortcomings of traditional filtering methods but also significantly improves the signal-to-noise ratio of the measured signal, thereby obtaining accurate and reliable measurement while drilling data. This measurement while drilling signal recognition technology is unaffected by the noise spectrum and effectively solves the problem of identifying measurement while drilling signals in mixed frequency conditions.

[0027] 2) This application obtains system parameters that match the noise intensity by adjusting the damping coefficient and system parameters, thereby achieving a system resonance output effect and improving the signal-to-noise ratio of the signal to be measured. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a flow chart of the method for frequency identification of measurement while drilling signals in this application.

[0029] Figure 2 This is a diagram of the stochastic resonance mechanism of the high-order bistable nonlinear system of this application.

[0030] Figure 3 This is the Am-D relationship diagram when the damping coefficient k=0.3, 0.5 and 0.9 of this application.

[0031] Figure 4 This is the Am-D relationship diagram when the system parameter a=0.36, 0.48 and 0.6 of this application.

[0032] Figure 5 This is the Am-D relationship diagram when the system parameter b=0.1, 0.15 and 0.2 of this application.

[0033] Figure 6 This is the output spectrum diagram of the high-order bistable parameter-adjusted stochastic resonance system of this application. DETAILED DESCRIPTION

[0034] The following is a clear and complete description of the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of them. Based on the embodiments of this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0035] like Figure 1 As shown, the present application provides a method for identifying the frequency of a measurement while drilling signal, comprising the following steps:

[0036] S1: The signal to be tested s ( t ) and noise n ( t ) Input the high-order bistable stochastic resonance system and set the appropriate conversion coefficient according to the frequency range of the measurement while drilling signal output by the high-order bistable stochastic resonance system R In this step, the transformation coefficients R The preferred setting is 100.

[0037] S2: Transform coefficient R The damping coefficient, system parameters and system output response in the high-order bistable stochastic resonance system are transformed to obtain the equivalent equation of the high-order bistable stochastic resonance system, which meets the small frequency application requirements of the high-order bistable stochastic resonance system.

[0038] S3: Detect noise intensityD Is it consistent with the signal to be tested? s ( t ) matches, if so, the signal is output directly and the signal to be tested is restored s ( t ) frequency; otherwise, the parameters of the high-order bistable stochastic resonance system are adjusted according to the parameter adjustment rules shown in Table 1.

[0039] Table 1 Parameter adjustment rules under different noise intensities

[0040]

[0041] In Table 1, Dop is the optimal noise intensity, k is the damping coefficient, a and b These are all system parameters.

[0042] S4: After achieving the stochastic resonance output effect, according to the transformation coefficient R Restore the signal to be tested s ( t ) frequency.

[0043] The specific steps of step S2 are as follows:

[0044] High-frequency signal recognition based on parameter-tuned stochastic resonance:

[0045] By the signal to be measured s ( t ) and noise n ( t ) are jointly driven by the high-order bistable stochastic resonance system as shown in formula (1):

[0046] x" ( t )+ kx' ( t )=-[ dU ( x ( t )) / dx ( t )]+ s ( t )+ n ( t )(1)

[0047] In formula (1), x ( t ) is the output response of the nonlinear system, which is the time t function; x' ( t )and x" ( t ) are respectively x (t )’s first and second derivatives; dU ( x ( t )) / dx ( t ) is the nonlinear restoring force; U ( x ( t )) is the potential function.

[0048] The potential function of the high-order bistable stochastic resonance system is shown in formula (2).

[0049] U ( x )=- ax 4 ( t ) / 4+ bx 6 ( t ) / 6(2)

[0050] Plotting the potential function U ( x ( t ))like Figure 2 As shown in the blue curve, it can be seen that it is a typical bistable potential field structure, which contains two potential wells and a potential barrier, and the overall potential function is about x ( t ) = 0. The motion state output by the system, that is, the Brownian particle eventually falls into a potential well after a transient process. The specific potential well it falls into is determined by the initial conditions of the system.

[0051] join in s ( t ) after which the system potential function is affected by the signal to be measured s ( t ) Periodic modulation, potential function U ( x ( t )) becomes V ( x ( t )):

[0052] V ( x ( t ))= U ( x ( t ))- x ( t )· s ( t )=- ax 4 ( t ) / 4+ bx6 ( t ) / 6- x ( t ) A sin(2 πf 0 t + φ )(3)

[0053] In the above formula, A 、 f 0 and φ The signals to be tested are s ( t )’s amplitude, frequency and initial phase.

[0054] At this time, the two potential wells of the potential function will be raised or lowered periodically, such as Figure 2 As shown by the black curve in the middle. Calculation shows that the system has a critical amplitude A C , so that the system maintains a bistable structure. A < A C When , the change of the potential well is not enough to make the potential barrier disappear, and the Brownian particle can only oscillate slightly in the single well. A > A C When the potential barrier changes with time, it may disappear, and the Brownian particle can cross the potential barrier and perform a large-scale transition motion between the two potential wells.

[0055] If you join at the same time s ( t )and n ( t ), Brownian particles make a large-scale transition motion between two potential wells with the help of noise, achieving A > A C The effect of movement, such as Figure 2 This is shown by the red curve in Figure 1. At this point, the signal to be measured, the noise, and the nonlinear system work synergistically. The noise no longer acts as an interference term, but instead transfers its high-frequency energy to the low-frequency signal to be measured, greatly enhancing its energy. At this point, the signal-to-noise ratio of the system output reaches its maximum, resulting in a stochastic resonance effect.

[0056] Furthermore, compared to traditional bistable systems, the potential function of higher-order systems has a greater height difference between the potential well and the potential barrier, requiring Brownian particles to experience stronger noise in order to achieve transitions. Consequently, higher-order bistable systems have a lower signal-to-noise ratio and better stability for their identifiable signals. This application selected higher-order bistable systems as both the research object and identification tool.

[0057] The present application adjusts the parameters of a high-order bistable stochastic resonance system, thereby realizing a measurement while drilling signal recognition method based on a parameter-adjusted stochastic resonance system.

[0058] The frequency value of the measurement while drilling signal is 1~3Hz. If the frequency of the measured signal is scaled to 0.01~0.03Hz, the small frequency limit of the high-order bistable stochastic resonance system is met. Therefore, this application sets the transformation coefficient R =100, scaled time scale t 1= R · t Rewriting formula (1) under the new time scale is as follows:

[0059] x" ( t 1)+ kx' ( t 1)= ax ( t 1) 3 - bx ( t 1) 5 + A sin(2 πf 1 t 1+ φ )+ n ( t 1)(4)

[0060] And the following relationship is satisfied

[0061] dt 1= R · dt (5)

[0062] x' ( t 1)= dx ( t 1) / dt 1= dx ( t 1) / Rdt = x' ( t ) / R (6)

[0063] x" ( t 1)= dx' ( t 1) / dt 1=[ dx' ( t 1) / R ] / Rdt = x" ( t ) / R2 (7)

[0064] Substituting formulas (5) to (7) into formula (4), the high-order bistable stochastic resonance system is calculated according to the transformation coefficient R From the new time scale t 1Restore to time scale t Then, we get the equivalent equation of formula (4):

[0065] x" ( t ) / R 2 + kx' ( t ) / R = ax ( t ) 3 - bx ( t ) 5 + A sin(2π f 0 t + φ )+ n ( t ) (8)

[0066] Transform coefficient R For the damping coefficient in formula (8) k , system parameters a and b And the system output response is transformed as follows:

[0067] k 1= R , a 1= R 6 a , b 1= R 10 b , x 1( t )= x ( t ) / R 2 (9)

[0068] In the above formula, k 1. a 1. b 1 and x 1( t ) are the transformed damping coefficient, system parameters and system output response respectively, f 1 is the corresponding frequency value under the new time scale.

[0069] From formula (9), we can get:

[0070] x' ( t )= dx / dt =( dx / dx 1)·( dx 1 / dt )= R 2 x 1 ' ( t )

[0071] x" ( t )= dx' ( t ) / dt =[ R 2 dx 1 ' ( t ) / dt ]= R 2 x 1 " ( t ) (10)

[0072] Substituting formulas (9) and (10) into formula (8), it can be equivalent to the following form:

[0073] x 1 " ( t )+ k 1 x 1 ' ( t )= a 1 x 1( t ) 3 - b 1 x 1( t ) 5 + A sin(2 πf 0 t + φ )+ n ( t )(11)

[0074] Formula (11) can realize the stochastic resonance of large frequency signals, that is, measurement while drilling signals. This application refers to formula (11) as a high-order bistable parameter-adjusted stochastic resonance system, and solves the defects of this method when applied to measurement while drilling signal identification through parameter adjustment.

[0075] The specific steps of step S3 are as follows:

[0076] According to the mechanism of stochastic resonance generated by the aforementioned high-order bistable stochastic resonance system, the migration ability of Brownian particles is determined by the noise intensity, the damping coefficient and the system parameters that determine the shape of the potential field. Therefore, the noise intensity can be matched by adjusting the parameters in formulas (1) and (2), so that the high-order bistable stochastic resonance system can achieve resonant output under any noise intensity. The adjustable parameters include the damping coefficient k and the system parameters that determine the potential well depth a and b , the adjustment steps are as follows:

[0077] 1) In formula (1) kx' The term represents the suppression of Brownian particle motion in the potential field, so the damping coefficient k is related to the optimal noise intensity that produces resonant output. Dop To verify this relationship, assuming that other parameters remain unchanged, the damping coefficients are set k Equal to 0.3, 0.5 and 0.9, the Am-D curve is as follows Figure 3 As shown. Am is the amplitude of the high-order bistable stochastic resonance system output at the frequency of the signal to be measured, and D represents the noise intensity. It can be seen that as the damping coefficient k As the damping coefficient increases, the optimal noise intensity that produces the resonant output effect also increases, that is, the energy required for the Brownian particle to undergo transition motion increases. k It does have an inhibitory effect on the transition motion of Brownian particles.

[0078] 2) In addition to the damping coefficient k In addition, the shape of the potential field will also affect the transition ability of Brownian particles. Through calculation, we know that the system parameters a The larger or parameter b The smaller it is, the deeper the potential well is, that is, the parameter a It has a negative effect on the transition ability of Brownian particles. b It has a positive effect on the transition ability of Brownian particles. Therefore, if the noise intensity of the measurement while drilling signal is too large, it can be improved by increasing the parameter a or decrease the value b To verify this relationship, assuming that other parameters remain unchanged, the coefficient parameters are set a =0.36, 0.48 and 0.6; b = 0.1, 0.15 and 0.2, the Am-D curves are as follows Figure 4 、 5 As shown in the figure, it can be seen that the optimal noise intensity to produce stochastic resonance effect is indeed related to the parametera Positively correlated with parameter b Negative correlation.

[0079] 3) By Figures 3-5 It can be seen that k Optimal noise intensity when changing Dop The corresponding Am value remains almost unchanged, because the damping coefficient k does not directly affect the transition ability of Brownian particles; on the other hand, the parameter a Increase or b When the optimal noise intensity is reduced Dop The corresponding Am value will decrease accordingly. Therefore, adjust the damping coefficient k When the noise intensity is matched, there is no significant effect on the output performance of the high-order bistable stochastic resonance system, while adjusting the system parameters a 、 b It will have a certain negative impact on the output performance of the system. Based on the above analysis, the damping coefficient should be k Set as the main adjustment parameter, a 、 b Set as auxiliary adjustment parameter.

[0080] The measurement while drilling signal is usually in an over-resonance state. Therefore, the parameter adjustment rules for over-resonance in Table 1 can be used for processing, thereby effectively solving the defects of this method when applied to measurement while drilling signal recognition.

[0081] Example

[0082] This example uses x The axis accelerometer measurement signal is used as the experimental object for test analysis. First, the collected data is discretized, and then the transformation coefficient is introduced R =100 to perform equivalent transformation on the high-order bistable stochastic resonance system; next, according to the parameter adjustment rules in Table 1, the damping coefficient k and system parameters a and b Adjust; finally, restore the frequency of the signal to be measured according to the transformation coefficient. After a large number of tests, it is found that the output spectrum of the high-order bistable parameter-adjusted stochastic resonance system is as follows: Figure 6 As shown in the figure, the amplitude of the system output spectrum at 2.4 Hz increases significantly, which is a typical example of stochastic resonance. This indicates that parameter adjustment can effectively identify the frequency value of the measurement while drilling signal, providing accurate sensor measurement data for subsequent steerable drilling tool attitude calculation.

[0083] Although the content of this application has been described in detail through the above preferred embodiments, it should be understood that the above description should not be considered as limiting the present application. After reading the above content, various modifications and substitutions of this application will be obvious to those skilled in the art. Therefore, the scope of protection of this application should be defined by the appended claims.

Claims

1. A method for frequency identification of measurement while drilling signals, characterized in that: The steps include: The signal to be measured s ( t ) and noise n ( t ) inputs a high-order bistable stochastic resonance system, and sets a conversion coefficient according to the frequency range of the measurement while drilling signal output by the high-order bistable stochastic resonance system R ; With the transformation coefficient R The damping coefficient in the high-order bistable stochastic resonance system k , system parameters a 、 b and system output response x Performing transformation to obtain an equivalent equation of the high-order bistable stochastic resonance system, wherein the equivalent equation meets the frequency application requirements of the high-order bistable stochastic resonance system; Detection noise intensity D Is it consistent with the signal to be tested? s ( t ) matches, if so, restore the signal to be tested s ( t Otherwise, according to the parameter adjustment rules of the high-order bistable stochastic resonance system parameter adjustment, to obtain a high-order bistable parameter adjustment stochastic resonance system, using the high-order bistable parameter adjustment stochastic resonance system to restore the measured signal s ( t ) frequency.

2. The method for identifying the frequency of a measurement while drilling signal according to claim 1, wherein: The high-order bistable stochastic resonance system is expressed as formula (1): x" ( t )+ kx' ( t )=-[ dU ( x ( t )) / dx ( t )]+ s ( t )+ n ( t )(1) In the above formula, x ( t ) is the output response of the nonlinear system; x' ( t )and x" ( t ) are respectively x ( t )’s first and second derivatives; dU ( x ( t )) / dx ( t ) is the nonlinear restoring force; U ( x ( t )) is the potential function, expressed as: U ( x ( t ))=- ax 4 ( t ) / 4+ bx 6 ( t ) / 6(2)。 3. The method for identifying the frequency of a measurement while drilling signal according to claim 1, wherein: The equivalent equation is expressed as formula (3): x 1 " ( t )+ k 1 x 1 ' ( t )= a 1 x 1( t ) 3 - b 1 x 1( t ) 5 + A sin(2 πf 0 t + φ )+ n ( t )(3) In the above formula, x 1( t ) is the response to the system output x ( t )The result after transformation, x 1 ' ( t )and x 1 " ( t ) are respectively x 1( t ), k 1 is the damping coefficient k The result after transformation, a 1 and b 1 are the system parameters a and b The result after transformation, A 、 f 0 and φ The signals to be tested are s ( t )’s amplitude, frequency and initial phase.

4. The method for identifying the frequency of a measurement while drilling signal according to claim 3, wherein: The damping coefficient is calculated according to the following formula: k , system parameters a 、 b and system output response x ( t ) to transform: k 1= R , a 1= R 6 a , b 1= R 10 b , x 1( t )= x ( t ) / R 2 。 5. The method for identifying the frequency of a measurement while drilling signal according to claim 1, wherein: The parameter adjustment rules are: When the resonance type is under-resonance, reduce the damping coefficient k , reduce system parameters a Or increase system parameters b ; When the resonance type is over-resonance, increase the damping coefficient k , increase system parameters a Or reduce system parameters b .

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