CN102928817A - Method for positioning rotor rubbing sound emission source by applying time delay estimation - Google Patents

Method for positioning rotor rubbing sound emission source by applying time delay estimation Download PDF

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CN102928817A
CN102928817A CN2012103974656A CN201210397465A CN102928817A CN 102928817 A CN102928817 A CN 102928817A CN 2012103974656 A CN2012103974656 A CN 2012103974656A CN 201210397465 A CN201210397465 A CN 201210397465A CN 102928817 A CN102928817 A CN 102928817A
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time delay
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acoustic emission
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CN102928817B (en
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邓艾东
童航
秦康
曹浩
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Southeast University
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Abstract

The invention discloses a method for positioning rotor rubbing sound emission source by applying time delay estimation, which comprises the following steps of: (10) building a one-dimensional linear positioning model; (20) setting a primary iteration value of attenuation coefficient estimation and a primary iteration value of time delay estimation; (30) calculating an estimation error between a real value and an estimation value; (40) calculating a next iterative step size according to the estimation error; (50) calculating iterated time delay estimation and attenuation coefficient estimation; (60) calculating a new estimation error; and (70) comparing relative error of the two estimation errors calculated in the step (30) and the step (60), measuring the position of the rubbing source according to delay time estimation if the relative error is smaller than a set value, or forwarding to the step (40) to continue iteration. According to the method, the problem of signal attenuation and strong noise interference during transmission of a rubbing sound emission signal of a rotor system is considered, and the rubbing fault source is accurately positioned by adding steps of attenuation estimation and changing the step size.

Description

Method for positioning rotor rubbing sound emission source by time delay estimation
Technical Field
The invention relates to a method for positioning a rotor rubbing sound emission source, in particular to a method for positioning the rotor rubbing sound emission source by time delay estimation.
Background
The friction of moving and static parts of a rotary machine is a common fault in operation. Especially, the current rotary machine is developing towards large-scale, high-parameter and high-efficiency, the equipment structure becomes more and more complex, and the dynamic and static gaps become smaller and smaller, so that the friction problem of the dynamic and static parts becomes more and more prominent. The Acoustic Emission technology (AE) is a method for effectively diagnosing rub-impact faults, can judge the occurrence of rub-impact and can calculate the position of the rub-impact by a positioning technology, and has important application value. Time Delay Estimation (TDE) is a method for estimating the Time difference of sound source signals arriving at different sensors, and at present, such algorithms mainly include Cross-Correlation (Cross-Correlation) algorithm, Generalized Cross-Correlation (GCC) algorithm, Recursive Least Square (RLS) algorithm, and Least Mean Square (LMS) algorithm, among which LMS adaptive Time Delay estimation is most commonly used. The LMS algorithm equates time delay as the signal passing through a finite impulse response filter, and uses a gradient descent method to continuously iterate time delay according to the difference between the filter output and the reference signal. However, the algorithm only tracks the time-varying signal-to-noise ratio, does not consider the attenuation of the signal, and generates a large error when being directly applied to the positioning of the AE source.
Disclosure of Invention
The technical problem is as follows: the technical problem to be solved by the invention is as follows: the method considers the problems of signal attenuation and strong noise interference in the transmission process of the rubbing acoustic emission signal of the rotor system, and more accurately realizes the positioning of the rubbing fault source by adding the steps of attenuation estimation and step length variation.
The technical scheme is as follows: in order to solve the technical problems, the invention adopts the technical scheme that:
a method for rotor rub-impact acoustic emission source localization using time delay estimation, the method comprising the steps of:
10): establishing a one-dimensional linear positioning model: the method comprises the following steps that a first sensor (1) and a second sensor (2) are arranged on a rub-impact wave guide plate of a rotor test bed, a rotor rub-impact source is located between the two sensors, the rotor rub-impact source and the two sensors are located on the same straight line, an acoustic emission signal is generated after the rotor rub-impact, the acoustic emission signal is received by the two sensors, and the acoustic emission signal is accompanied with attenuation and noise interference in the transmission process;
20): setting attenuation coefficient estimationInitial iteration value and time delay estimation ofInitial iteration value of (a): collecting acoustic emission signals x (t) received by a first sensor (1) and acoustic emission signals y (t) received by a second sensor (2) by using a rub-impact acoustic emission testing device, and then taking the energy ratio of the two acoustic emission signals as an attenuation coefficient to estimate
Figure BDA00002274176500023
Initial iteration value of, finally, setting a time delay estimate
Figure BDA00002274176500024
The initial iteration value of (a);
30): measuring and calculating the estimation error between the true value and the estimated value of y (t): assuming that the energy of y (t) is less than that of x (t) in the two acoustic emission signals, the rub-impact source signal reaches the first sensor (1) first, and then reaches the second sensor (2) after a delay time delta tau, and then the estimation error of the true value and the estimated value of y (t) is measured according to the formula (1):
e ( t ) = y ( t ) - α ^ x ( t - Δ τ ^ ) formula (1)
Wherein e (t) represents an estimation error,
Figure BDA00002274176500026
an attenuation coefficient estimate representing the true attenuation coefficient alpha,
Figure BDA00002274176500027
a time delay estimate representing the true time delay deltatau,
Figure BDA00002274176500028
representing the signal received by the second sensor (2), the signal x (t) received by the first sensor (1) being delayed in time
Figure BDA00002274176500029
The subsequent signal;
40): according to the estimation error e (t), calculating the step length of the next iteration;
50): measuring and calculating time delay estimation and attenuation coefficient estimation after iteration according to the formula (2);
Δ α ^ ( t + 1 ) = Δ α ^ ( t ) - μ α e ( t ) d ( e ( t ) ) d ( Δ α ^ ( t ) ) Δ τ ^ ( t + 1 ) = Δ τ ^ ( t ) - μ Δτ e ( t ) d ( e ( t ) ) d ( Δ τ ^ ( t ) ) formula (2)
Wherein,
Figure BDA00002274176500031
representing the estimate of the attenuation coefficient after the iteration,
Figure BDA00002274176500032
representing the attenuation coefficient estimate, mu, before iterationαTo represent
Figure BDA00002274176500033
The step size of the iteration of (a),
Figure BDA00002274176500034
representing the partial derivatives of the attenuation coefficient estimates before iteration,
Figure BDA00002274176500035
representing the time delay estimate after the iteration,representing the time delay estimate before iteration, μ ΔτTo represent
Figure BDA00002274176500037
The step size of the iteration of (a),
Figure BDA00002274176500038
representing a partial derivative of an estimate of the time delay before the iteration;
60): substituting the time delay estimation after iteration and the attenuation coefficient estimation after iteration, which are measured and calculated in the step 50), into an equation (1), and measuring and calculating a new estimation error e (t + 1);
70): comparing the relative error of the two estimation errors measured in the step 30) and the step 60), wherein the relative error is
Figure BDA00002274176500039
If the relative error is less than 1%, stopping measuring and calculating, taking the time delay estimation measured in the step 50) as the real time delay delta tau, and measuring the position of the rub-impact source according to the formula (3); if the relative error is more than or equal to 1%, replacing e (t) in the step 30) with a new estimation error e (t +1) calculated in the step 60), and then repeating the step 40) to the step 70);
S1(D-v Δ τ)/2 formula (3)
Wherein S is1D represents the distance between the first sensor (1) and the second sensor (2), v represents the propagation speed of the acoustic emission wave, and delta tau represents the time difference of the acoustic emission wave reaching the two sensors.
Has the advantages that: compared with the prior art, the invention has the following advantages:
(1) and the positioning of the rubbing fault source is accurately realized. The invention considers the attenuation factor of the acoustic emission signal in the rotor system rebroadcasting process, and adopts the band attenuation estimation in the positioning process. The method can obviously improve the estimation performance of the time delay parameter at the time of low signal-to-noise ratio, and obviously improve the positioning accuracy of the rub-impact source.
(2) The convergence speed is accelerated, and the measuring and calculating efficiency is improved. The variable step length method provided by the invention can effectively accelerate the convergence speed of LMS, so that the estimation system has better robustness, the steady state detuning amount is reduced, the time-varying tracking capability of the algorithm is effectively improved, and the real-time positioning requirement is better met. The performance of the LMS algorithm at low signal-to-noise ratio can be obviously improved, the LMS algorithm has higher convergence rate, and the time delay estimation precision is improved.
Drawings
Fig. 1 is a schematic diagram of the present invention.
FIG. 2 is a schematic diagram of the one-dimensional linear positioning model established in step 10) of the present invention.
FIG. 3 is a waveform diagram of AE of a section of continuous rubbing received by the first sensor of the present invention when the rotor speed is 2040 r/min.
FIG. 4 is a waveform diagram of AE waveform of a section of continuous rubbing received by the second sensor in the present invention when the rotor speed is 2040 r/min.
FIG. 5 is an expanded view of a cluster of AE waveforms in FIG. 3.
FIG. 6 is an expanded view of a cluster of AE waveforms of FIG. 4.
FIG. 7 shows the time delay and attenuation coefficient iteration curve of LMS with attenuation estimation in the experiment of the present invention when the SNR is 10 dB.
FIG. 8 is an iterative graph of the conventional LMS and LMS with attenuation estimation at a signal-to-noise ratio of 0dB in the experiment of the present invention.
FIG. 9 is an iterative graph of the conventional LMS and the method of the present invention for a signal-to-noise ratio of 0dB in the experiment of the present invention.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings and the examples.
Referring to fig. 1 and 2, a method for locating a rotor rub-on acoustic emission source using time delay estimation according to the present invention comprises the steps of:
10): establishing a one-dimensional linear positioning model: the method is characterized in that a first sensor 1 and a second sensor 2 are arranged on a rub-impact wave guide plate of a rotor test bed, a rotor rub-impact source is located between the two sensors, the rotor rub-impact source and the two sensors are located on the same straight line, an acoustic emission signal is generated after the rotor rub-impact, the acoustic emission signal is received by the two sensors, and the acoustic emission signal is accompanied with attenuation and noise interference in transmission.
In the step 10), the rotor rub-impact acoustic emission signal is obtained through a rotor rub-impact test stand. The friction collision between moving and static parts is simulated by a movable friction collision support arranged on a base of the rotor platform, a telescopic friction collision screw is arranged on the support, the friction collision screw is positioned on the side surface of the disc and radially faces the center of the rotating shaft along the shaft, and friction collision faults of different degrees can be simulated by adjusting the friction collision screw. The AE signals generated by the rubbing source are transmitted to the AE sensors on two sides, namely the first sensor 1 and the second sensor 2, through the wave guide plate. The first sensor 1 and the second sensor 2 adopt UT-1000 broadband sensors, the signal acquisition system is a PCI-2 acquisition device and matched software, the resolution ratio of 18 bits A/D is high, and the frequency response range is 1kHz-3 MHz. The wave velocity was estimated in advance from the simulated rub-impact AE waveform at static conditions. When the rotor rotates for one circle in a dynamic state, the rotor and the rubbing screw rub once to form a cluster of AE waves, so that AE signals have periodicity when the rotor continuously rubs. FIG. 3 is an AE waveform of a section of continuous rubbing received by the first sensor 1 when the rotor speed is 2040r/min, FIG. 4 is an AE waveform of a section of continuous rubbing received by the second sensor 2 when the rotor speed is 2040r/min, and FIG. 5 is an expanded view of a cluster of AE waveforms in FIG. 3. FIG. 6 is an expanded view of a cluster of AE waveforms of FIG. 4. The difference in distance from the source of the rub-impact to the two sensors in this experiment was 184 mm.
20): setting attenuation coefficient estimationInitial iteration value and time delay estimation ofInitial iteration value of (a): collecting acoustic emission signals x (t) received by a first sensor 1 and acoustic emission signals y (t) received by a second sensor 2 by using a rub-impact acoustic emission testing device, and then taking the energy ratio of two paths of acoustic emission signals as an attenuation coefficient to estimate
Figure BDA00002274176500053
Initial iteration value of, finally, setting a time delay estimate
Figure BDA00002274176500054
The initial iteration value of (a).
In step 20), attenuation coefficient estimation
Figure BDA00002274176500055
The initial iteration value of (2) is measured as follows: calculating the energy sum of x (t) and the energy sum of y (t) in the same time period, dividing the smaller value of the energy sum by the larger value to obtain the ratio of the two values, namely the energy ratio of the two sensors, wherein the energy ratio is less than 1, and the energy ratio is the attenuation coefficient estimationThe initial iteration value of (a). At the same time, a time delay value is given
Figure BDA00002274176500057
An initial iteration value. Since the acquisition signal is a discrete time series, the given time delay value is a certain data point value.
30): measuring and calculating the estimation error between the true value and the estimated value of y (t): assuming that the energy of y (t) is less than the energy of x (t) in the two acoustic emission signals, the rub-impact source signal reaches the first sensor 1 first, and then reaches the second sensor 2 after a delay time Δ τ, and then the estimation error between the true value and the estimated value of y (t) is measured according to the formula (1):
e ( t ) = y ( t ) - α ^ x ( t - Δ τ ^ ) formula (1)
Wherein e (t) represents an estimation error,
Figure BDA00002274176500059
an attenuation coefficient estimate representing the true attenuation coefficient alpha,
Figure BDA000022741765000510
a time delay estimate representing the true time delay delta tau,representing the signal received by the second sensor (2), the signal x (t) received by the first sensor (1) being delayed in timeThe latter signal.
40): and calculating the step length of the next iteration according to the estimation error e (t).
In step 40), when the estimation error e (t) calculated in step 30) is greater than 0.1, the iteration step size is calculated according to equation (4),
μ α ( t + 1 ) = b α [ 1 - exp ( - a α | ▿ α | ) ] μ Δτ ( t + 1 ) = b Δτ [ 1 - exp ( - a Δτ | ▿ ▿ τ | ) ] formula (4)
When the estimation error e (t) is less than or equal to 0.1, the iteration step is calculated according to the formula (5),
μ α ( t + 1 ) = b α { 1 - exp [ - a α ϵ ( t ) ] } μ Δτ ( t + 1 ) = b Δτ { 1 - exp [ - a Δτ ϵ ( t ) ] } formula (5)
Wherein, muα(t +1) represents a novel
Figure BDA00002274176500065
Iteration step size, μΔτ(t +1) represents a novel
Figure BDA00002274176500066
Iteration step size of aα、bα、aΔτAnd bΔτAll are step size adjustment factors, epsilon (t) represents the error obtained after linear weighting of the error matrix,
Figure BDA00002274176500067
representing the gradient of the estimation error e (t) for the attenuation coefficient,representing the gradient of the estimation error e (t) with respect to the time delay.
The iteration step size determines the calculated convergence speed to a certain extent. In order to accelerate the convergence rate of the measurement and calculation, when an expected error is large, a larger iteration step length is adopted, so that the measurement and calculation can be quickly close to a true value; when the error is small, the oscillation of the estimated value at the true value is reduced by adopting a smaller step length, and the error during convergence is reduced. The current step size changing method generally adjusts the step size directly according to the size of the error or adjusts the step size by using the number of iterations. However, these methods are greatly affected when noise is strongly changed, and the convergence speed is slow. The invention provides that when the estimation error is larger, the step length is adjusted by using the gradient of the error, when the error is smaller, a forgetting factor is introduced to weight the error at the previous moment, and the step length is adjusted by using the weighted error.
When the estimation error is larger than 0.1, the adjustment method of the iteration step size is as follows:
Figure BDA00002274176500069
representing the gradient of the estimation error e (t) for the attenuation coefficient, representing the gradient of the estimation error e (t) with respect to the time delay,the iteration step size is as shown in equation (4) above.
When the estimation error is less than or equal to 0.1, the adjustment method of the iteration step size is as follows: defining forgetting matrix λ ═ λL λL-1…λ0]Wherein λ isiI is more than or equal to 0 and less than or equal to L. The forgetting matrix has the function of carrying out nonlinear weighting on all errors with the previous time length of L, and the closer the forgetting matrix is to the current moment, the larger the forgetting factor is, and the larger the influence on the weighted errors is. The forgetting factor takes the form of an exponential decay, λi＝ciC is a constant close to 1, 0 < c < 1. The weighted error is denoted as ε (t), e (t) ═ e (t) λTWherein e (t) is an error matrix with a time length L before time t, and e (t) is [ e (t-L +1) L e (t-1) e (t)]The step length adjustment method is shown in formula (5).
50): measuring and calculating time delay estimation and attenuation coefficient estimation after iteration according to the formula (2);
&Delta; &alpha; ^ ( t + 1 ) = &Delta; &alpha; ^ ( t ) - &mu; &alpha; e ( t ) d ( e ( t ) ) d ( &Delta; &alpha; ^ ( t ) ) &Delta; &tau; ^ ( t + 1 ) = &Delta; &tau; ^ ( t ) - &mu; &Delta;&tau; e ( t ) d ( e ( t ) ) d ( &Delta; &tau; ^ ( t ) ) formula (2)
Wherein,representing the estimate of the attenuation coefficient after the iteration,
Figure BDA00002274176500074
representing the attenuation coefficient estimate, mu, before iterationαTo represent
Figure BDA00002274176500075
The step size of the iteration of (a),
Figure BDA00002274176500076
representing the partial derivatives of the attenuation coefficient estimates before iteration,
Figure BDA00002274176500077
representing the time delay estimate after the iteration,
Figure BDA00002274176500078
representing the time delay estimate, mu, before the iterationΔτTo represent
Figure BDA00002274176500079
The step size of the iteration of (a),
Figure BDA000022741765000710
representing the partial derivative of the time delay estimate before the iteration.
60): substituting the time delay estimation after iteration and the attenuation coefficient estimation after iteration, which are measured and calculated in the step 50), into an equation (1), and measuring and calculating a new estimation error e (t + 1).
70): comparing the relative error of the two estimation errors measured in the step 30) and the step 60), wherein the relative error is
Figure BDA000022741765000711
If the relative error is less than 1%, stopping measuring and calculating, taking the time delay estimation measured in the step 50) as the real time delay delta tau, and measuring the position of the rub-impact source according to the formula (3); if the relative error is more than or equal to 1%, replacing e (t) in the step 30) with a new estimation error e (t +1) calculated in the step 60), and then repeating the step 40) to the step 70);
S1(D-v Δ τ)/2 formula (3)
Wherein S is1D represents the distance between the first sensor (1) and the second sensor (2), v represents the propagation speed of the acoustic emission wave, and delta tau represents the time difference of the acoustic emission wave reaching the two sensors.
The method adopts the least mean square self-adaptive time delay estimation with attenuation estimation and variable step length to calculate the time delay, and improves the precision of positioning the rub-impact source. This is demonstrated experimentally below.
When the step length is a fixed value, the actual effect of the LMS is estimated by the attenuation:
gaussian white noise with different signal-to-noise ratios was added to the waveforms of fig. 3 and 4 to simulate a field actual noisy AE signal. And (3) carrying out time delay estimation on the AE signal containing the noise and the rub by using an LMS algorithm with step length fixed value and attenuation estimation, wherein experimental parameters are as follows:
signal sampling frequency: 512 kHz;
the time delay iteration step length is as follows: 0.05;
attenuation coefficient iteration step size: 0.01;
initial iteration value of time delay: 100, respectively;
signal-to-noise ratio: 10 dB.
The real time delay is calculated by measuring the distance difference between the collision and friction source and the two sensors and the wave speed, and is 575 time delay points. And comparing the total energy of the two sections of signals in the same time to obtain the attenuation coefficient of the signals. Fig. 7 shows the result of the iteration, after 1200 steps, although the attenuation coefficient has not converged to the true value, the estimate of the time delay has converged. The LMS is a noise cancellation algorithm in nature, and in practical applications, a part of signals may be cancelled out, or a certain amount of noise still exists after cancellation, which is a cause of an estimation error of the attenuation coefficient.
FIG. 8 is a comparison graph of the iteration curves of the conventional LMS and the LMS with attenuation estimation when 0dB SNR noise is added to the two signals. It can be seen that the conventional LMS cannot converge to the true value as the signal-to-noise ratio decreases, whereas the method with fading estimation of the present invention can converge to the true value. When the homologous rub-impact AE signals are transmitted to different sensors, due to the distance difference, the signals received by the sensors at a far distance are necessarily attenuated, the noise received by each sensor is of the same energy level, and no attenuation exists between the sensors, and the effect of estimating the attenuation is that the LMS can better offset the noise of the same energy level, so that the noise interference resistance in the positioning process is improved.
The actual effect of the LMS is estimated by the variable-step band attenuation: when the estimation error is larger than 0.1, the step size is determined by adopting the gradient of the error, and when the estimation error is smaller than 0.1, a forgetting factor is introduced to weight the error so as to determine the step size. The forgetting factor c is taken to be 0.95, and the forgetting matrix length L is 20. As can be seen from fig. 9, the LMS with variable step size converges after 300 steps of iteration, whereas the LMS without variable step size converges after 1200 steps, and the tracking capability of the measurement and calculation is significantly improved.

Claims (2)

  1. A method for rotor rub-impact acoustic emission source localization using time delay estimation, comprising the steps of:
    10): establishing a one-dimensional linear positioning model: the method comprises the following steps that a first sensor (1) and a second sensor (2) are arranged on a rub-impact wave guide plate of a rotor test bed, a rotor rub-impact source is located between the two sensors, the rotor rub-impact source and the two sensors are located on the same straight line, an acoustic emission signal is generated after the rotor rub-impact, the acoustic emission signal is received by the two sensors, and the acoustic emission signal is accompanied with attenuation and noise interference in the transmission process;
    20): setting attenuation coefficient estimation
    Figure FDA0000227417641
    Initial iteration value and time delay estimation of
    Figure FDA0000227417642
    Initial iteration value of (a): collecting acoustic emission signals x (t) received by a first sensor (1) and acoustic emission signals y (t) received by a second sensor (2) by using a rub-impact acoustic emission testing device, and then taking the energy ratio of the two acoustic emission signals as an attenuation coefficient to estimate
    Figure FDA0000227417643
    Initial iteration value of, finally, setting a time delay estimate
    Figure FDA0000227417644
    The initial iteration value of (a);
    30): measuring and calculating the estimation error between the true value and the estimated value of y (t): assuming that the energy of y (t) is less than that of x (t) in the two acoustic emission signals, the rub-impact source signal reaches the first sensor (1) first, and then reaches the second sensor (2) after a delay time delta tau, and then the estimation error of the true value and the estimated value of y (t) is measured according to the formula (1):
    Figure FDA0000227417645
    formula (1)
    Wherein e (t) represents an estimation error,
    Figure FDA0000227417646
    an attenuation coefficient estimate representing the true attenuation coefficient alpha,
    Figure 2012103974656100001DEST_PATH_IMAGE001
    a time delay estimate representing the true time delay deltatau,
    Figure FDA0000227417648
    representing the signal received by the second sensor (2), the signal x (t) received by the first sensor (1) being delayed in time
    Figure 855877DEST_PATH_IMAGE001
    The subsequent signal;
    40): according to the estimation error e (t), calculating the step length of the next iteration;
    50): measuring and calculating time delay estimation and attenuation coefficient estimation after iteration according to the formula (2);
    Figure FDA00002274176410
    formula (2)
    Wherein,
    Figure FDA00002274176411
    representing the estimate of the attenuation coefficient after the iteration,
    Figure FDA00002274176412
    representing the attenuation coefficient estimate, mu, before iterationαTo represent
    Figure FDA00002274176413
    The step size of the iteration of (a),
    Figure 2012103974656100001DEST_PATH_IMAGE002
    representing the partial derivatives of the attenuation coefficient estimates before iteration,
    Figure FDA00002274176415
    representing the time delay estimate after the iteration,
    Figure FDA00002274176416
    representing the time delay estimate, mu, before the iterationΔτTo represent
    Figure 835334DEST_PATH_IMAGE001
    The step size of the iteration of (a),
    Figure 2012103974656100001DEST_PATH_IMAGE003
    representing a partial derivative of an estimate of the time delay before the iteration;
    60): substituting the time delay estimation after iteration and the attenuation coefficient estimation after iteration, which are measured and calculated in the step 50), into an equation (1), and measuring and calculating a new estimation error e (t + 1);
    70): comparing the relative error of the two estimation errors measured in the step 30) and the step 60), wherein the relative error is
    Figure 2012103974656100001DEST_PATH_IMAGE004
    If the relative error is less than 1%, stopping measuring and calculating, taking the time delay estimation measured in the step 50) as the real time delay delta tau, and measuring the position of the rub-impact source according to the formula (3); if the relative error is more than or equal to 1%, replacing e (t) in the step 30) with a new estimation error e (t +1) calculated in the step 60), and then repeating the step 40) to the step 70);
    S1= D (D-v. DELTA. tau)/2 formula (3)
    Wherein S is1D represents the distance between the first sensor (1) and the second sensor (2), v represents the propagation speed of the acoustic emission wave, and delta tau represents the time difference of the acoustic emission wave reaching the two sensors.
  2. 2. The method for rotor rub-impact acoustic emission source localization according to claim 1, wherein in said step 40), when the estimation error e (t) calculated in step 30) is greater than 0.1, the iterative step is calculated according to equation (4),
    Figure FDA00002274176420
    formula (4)
    When the estimation error e (t) is less than or equal to 0.1, the iteration step is calculated according to the formula (5),
    Figure FDA00002274176421
    formula (5)
    Wherein, muα(t +1) represents a novel
    Figure FDA00002274176422
    Iteration step size, μΔτ(t +1) represents a novel
    Figure 615072DEST_PATH_IMAGE001
    Iteration step size of aα、bα、a△τAnd b△τAll are step size adjustment factors, epsilon (t) represents the error obtained after linear weighting of the error matrix,
    Figure FDA00002274176424
    representing the gradient of the estimation error e (t) for the attenuation coefficient,
    Figure FDA00002274176425
    representing the gradient of the estimation error e (t) with respect to the time delay.
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CN105891810A (en) * 2016-05-25 2016-08-24 中国科学院声学研究所 Fast adaptive joint time delay estimation method
CN106596088A (en) * 2016-12-13 2017-04-26 东南大学 Rub-impact sound emission fault position identification method based on near field sound source focusing positioning
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