WO1998048508A2 - Procede et appareil de reduction active multivoie du bruit et des vibrations - Google Patents

Procede et appareil de reduction active multivoie du bruit et des vibrations Download PDF

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WO1998048508A2
WO1998048508A2 PCT/US1998/007920 US9807920W WO9848508A2 WO 1998048508 A2 WO1998048508 A2 WO 1998048508A2 US 9807920 W US9807920 W US 9807920W WO 9848508 A2 WO9848508 A2 WO 9848508A2
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zeros
lms
equation
algorithm
filtered
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PCT/US1998/007920
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WO1998048508A3 (fr
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Scott C. Douglas
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University Of Utah Research Foundation
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Publication of WO1998048508A3 publication Critical patent/WO1998048508A3/fr

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    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10K—SOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
    • G10K11/00—Methods or devices for transmitting, conducting or directing sound in general; Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/16—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/175—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound
    • G10K11/178—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase
    • G10K11/1785—Methods, e.g. algorithms; Devices
    • G10K11/17853—Methods, e.g. algorithms; Devices of the filter
    • G10K11/17854—Methods, e.g. algorithms; Devices of the filter the filter being an adaptive filter
    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10K—SOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
    • G10K11/00—Methods or devices for transmitting, conducting or directing sound in general; Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/16—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/175—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound
    • G10K11/178—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase
    • G10K11/1787—General system configurations
    • G10K11/17879—General system configurations using both a reference signal and an error signal
    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10K—SOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
    • G10K11/00—Methods or devices for transmitting, conducting or directing sound in general; Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/16—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/175—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound
    • G10K11/178—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using interference effects; Masking sound by electro-acoustically regenerating the original acoustic waves in anti-phase
    • G10K11/1787—General system configurations
    • G10K11/17879—General system configurations using both a reference signal and an error signal
    • G10K11/17881—General system configurations using both a reference signal and an error signal the reference signal being an acoustic signal, e.g. recorded with a microphone
    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10K—SOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
    • G10K2210/00—Details of active noise control [ANC] covered by G10K11/178 but not provided for in any of its subgroups
    • G10K2210/30—Means
    • G10K2210/301—Computational
    • G10K2210/3012—Algorithms
    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10K—SOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
    • G10K2210/00—Details of active noise control [ANC] covered by G10K11/178 but not provided for in any of its subgroups
    • G10K2210/30—Means
    • G10K2210/301—Computational
    • G10K2210/3026—Feedback
    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10K—SOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
    • G10K2210/00—Details of active noise control [ANC] covered by G10K11/178 but not provided for in any of its subgroups
    • G10K2210/30—Means
    • G10K2210/301—Computational
    • G10K2210/3027—Feedforward
    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10K—SOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
    • G10K2210/00—Details of active noise control [ANC] covered by G10K11/178 but not provided for in any of its subgroups
    • G10K2210/30—Means
    • G10K2210/301—Computational
    • G10K2210/3053—Speeding up computation or convergence, or decreasing the computational load

Definitions

  • the present invention was at least partially funded by DARPA Grant No. DAAH04-96-1-0085
  • the present invention relates to a method and apparatus for improved active noise and vibration control. More specifically, intentional delay is introduced into a feedback loop to thereby reduce complexity of the equations, and then the invention compensates for the intentionally induced delay to thereby realize the benefits of the reduced complexity of the system.
  • ANVC Active noise and vibration control
  • DSP digital signal processing
  • MAC multiply/accumulate
  • the filtered-X algorithm " is a modification of the basic feedforward LMS algorithm.
  • the modification is required when dynamics exist between the adaptive filter output and the error sensor signals.
  • the modification to the update equation includes an estimate of the plant transfer function.
  • the filtered-X LMS algorithm suffers from at least one drawback that makes it difficult to implement when a multichannel controller is desired: the complexity of the coefficient updates for the finite-impulse-response (FIR) filters within the controller in this situation is often much greater than the complexity of the input-output calculations . It is not unusual for the coefficient updates to require more than ten times the number of MACs needed to compute the outputs of the controller for fixed coefficient values, and the situation worsens as the number of error sensors is increased. For this reason, recent efforts have focused on ways to reduce the complexity of the filtered-X LMS algorithm in a multi-channel context.
  • FIR finite-impulse-response
  • Some of the suggested changes to reduce complexity include: (1) block processing of the coefficient updates using fast convolution techniques, (2) partial updating of the controller coefficients, and (3) filtered-error methods. While useful, these methods often reduce the overall convergence performance of the controller, either because they introduce additional delays into the coefficient update loop or because they throw away useful information about the state of the control system. Such a performance loss may not be tolerable in some applications .
  • the multichannel filtered-X LMS algorithm also suffers from excessive data storage requirements.
  • This algorithm employs filtered input signal values that are created by filtering every input signal by every output-actuator-to- error-sensor channel of the acoustic plant.
  • the number of these terms can be an order-of-magnitude greater than the number of controller coefficients and input signal values used in the input-output calculations .
  • system designers may be forced to use costly off-chip memory within their controller architectures that can further slow the operation of the system due to limits in input/output data throughput. While some of the aforementioned techniques for complexity reduction also have reduced memory requirements, the performance of the overall system is effectively limited by these methods.
  • the sensitivity of the controller's performance to the feedback error signals is propagated back to the controller states through a brute-force calculation step.
  • the present invention accumulate the sensitivities of the error signals to the state of the controller in such a way as to avoid this costly recombination step with its order-of-magnitude increase in the number of instructions per sample time.
  • the present invention is realized in a method and apparatus for implementing a fast, exact implementation of a filtered-X LMS adaptive filter for which the system's complexity scales according to the number of filter coefficients within the system.
  • a mathematically equivalent controller system intentionally introduces a delay in a feedback signal to thereby reduce the number of calculations necessary to calculate coefficients.
  • the system then utilizes delay compensation to overcome the effects of the delay, resulting in an system which generates the same results as a more costly and computationally more intensive controller system.
  • the delay compensation technique in a single channel system is useful where the output actuators are located close to the error signals and far away from the input sensors .
  • the separability of the computations makes the new algorithm beneficial in all multichannel controller systems except those with only a coupled of controller channels .
  • Figure 1 is a block diagram of a prior art single- channel filtered-X LMS adaptive controller.
  • FIG. 2 is a block diagram of a preferred embodiment which is made in accordance with the principles of the present invention, and shows a single- channel LMS adaptive controller employing delay compensation .
  • Figure 3A is a simulated performance of the present invention on air compressor noise when there is an unattenuated noise power.
  • Figure 3B is a simulated performance of the present invention on air compressor noise when there is residual noise power for the adjoint LMS/CPFE (corrected phase filtered error) , fast filtered-X LMS, and fast LMS algorithms .
  • Figure 3C is a simulated performance of the present invention on air compressor noise when there is residual noise power for the fast filtered-X LMS and fast LMS algorithms with stabilization.
  • the present invention is a fast, exact implementation of an adaptive filter for which the system's complexity scales according to the number of filter coefficients within the system. Furthermore, the present invention extends computationally-efficient methods for effectively removing the delays of the secondary paths within the coefficient updates. The present invention accomplishes these tasks using algorithms which are mathematically equivalent to the original filtered-X LMS algorithm.
  • Figure 1 shows a block diagram of a controller system implementing a single-channel filtered-X LMS algorithm.
  • a sensor is placed near a noise source to collectb samples of the input signal ⁇ (n) for processing by the system.
  • This system computes an actuator output signal y(n) using a time-varying FIR filter of the form:
  • Equation (1) L- ⁇
  • V( n ) ⁇ u>.(n)x(n - 0,
  • d (n) is the unattenuated noise signal
  • Equation (2) is never computed because e (n) is a measurement of a physical quantity.
  • equation (1) this is the input-output relationship for the controller.
  • the controller computes y(n) to create anti-noise or anti-vibration.
  • the calculation represented by equation (1) must be performed at each sample time. In the present invention, this equation is effectively not reduced, but is the same as the prior art algorithm.
  • equation (2) this equation describes a physical process which occurs. Consequently, equation (2) mathematically defines an accurate model. Therefore, this is something which is not computed, it is just measured. The quantity is measured by the error microphone or error sensors. Therefore, the result of equation (2) is the input from the error sensors.
  • the values of hm used in equation (4) are estimates of the actual hm in equation (2) and are usually obtained in a separate estimation procedure that is performed prior to the application of control.
  • equation (3) this equation will be different from the prior art filtered-X LMS algorithm. It describes how the quantity w is being changed by way of coefficients (parameters, numerical values stored in memory) . It is necessary to store 1 parameters, where 1 represents filter length. These values for w are calculated for each sample time. Where the quantities in equation (3) are fixed numbers or measured values, the quantity being calculated is /(n-1).
  • equation (4) this equation is very similar to the input-output equation of the controller introduced in equation (1) .
  • the parameter h m must be performed at each sample time.
  • the new algorithm is essentially a change in the way that equations (3) and (4) are calculated. Most importantly, the present invention does not calculate equation (4) at all. Consequently, there are realized substantial savings in memory space because of the elimination of the calculations required to obtain the result of equation (4) .
  • the present invention essentially changes the way that the result of equation (3) is updated. This in turn affects the way in which equation (1) is calculated.
  • the present invention will now be shown in this embodiment as a modified implementation of the single channel filtered-X LMS algorithm.
  • This method combines the adjoint LMS/corrected phase filtered error (CPFE) algorithm with a method for delay compensation used in fast projection adaptive filters.
  • CPFE phase filtered error
  • the coefficient updates of the original algorithm are in the form of
  • Equation (10) t
  • (n) i ⁇
  • Equation (9) indicates an important fact about the structure of the filtered-X LMS updates: the same input sample x(n — ⁇ - m ) is used in successive time instants to update the same coefficient w ⁇ (n) .
  • This structure is exploited to develop a set of coefficient updates that are grouped according to the individual x(n — ⁇ - m) values appearing on the right-hand- side of equation (9) .
  • Such a scheme updates the 1th auxiliary coefficient w ⁇ (n) rather than the actual controller coefficient w ⁇ (n) .
  • em(n) as m
  • Equation (12) is essentially a replacement for equation (3) of the prior art.
  • Equation (12) basically updates coefficients in a very different manner by multiplying x by a quantity e M .
  • the most significant difference then is that new equation (12) does not use /(n) in the updating. Consequently, /(n) no longer needs to be computed, thus eliminating the computation of equation (4) .
  • What does need to be computed is the new value e M .
  • the quantity e M is defined in equation (11) .
  • the result of equation (11) is defined, again, in terms of ⁇ . Therefore, the algorithm proceeds where the sequence of calculations performed is equation (6), then equation (11), then equation (12) . In other words, equations (6), (11) and (12) replace equations . (3) and (4).
  • Equation (16) A problem is that a different update quantity is the result in equation (12) . Therefore, y is now calculated in a new way.
  • the new equation for y is shown in equation (16) .
  • the first summation is similar to the original term in equation (1) .
  • the second summation is a new term which is defined as the delay compensation term.
  • the terms of the second summation are defined in equations (17) and (18) .
  • equation (12) is the single-channel version of the adjoint LMS/CPFE algorithm. What is novel is the relationship in equation (9) that provides the link between w ⁇ (n) and w ⁇ (n) , or, equivalently, the link between the adjoint LMS/CPFE and filtered-X LMS algorithms. Equation (9) is used to compute y(n) for the filtered-X LMS algorithm using w ⁇ (n) as calculated by equation (12). To proceed, the expression for w ⁇ (n + 1) is substituted in equation (7) into equation (9). Using equation (11) , the equation obtained is
  • Equation (15): rm ( n ) - x(n - I - ro) ⁇ (n - /). l o
  • equation (11) could be simplified. This new equation is shown in equations (18) and (19) .
  • equation (16) thus now includes the delay compensation term.
  • the delay introduced into the algorithm is introduced in equation (12) in the term of e M (n) .
  • This term is a filtered or delayed version (at different values of frequency or amplitude) of the original signal epsilon.
  • the result of equation (12) is not what is wanted. Nevertheless, it is possible to compensate for the delay through equation (16) and still obtain the output. Therefore, the result of equation (16), y(n), is mathematically identical to the y(n) of equation (1) of the prior art. Numerically, they will of course be slightly different because of numerical inaccuracies introduced in calculations because of the precision of the computing device.
  • I input sensors are used to collect I input signals x (i) (n) , l ⁇ i ⁇ I .
  • the controller computes J output signals y' j> (n) , 1 ⁇ j ⁇ J , as
  • Equation ( 20 ) y (i)( n ) - /), where w ⁇ 1 - ⁇ (n) , 0 ⁇ / ⁇ -l are the L FIR filter coefficients for the ith-input-to- ' th-output channel of the controller.
  • the J " controller output signals propagate to the desired quiet region, where K error sensors measure the error signals e ⁇ k> (n) , l ⁇ k ⁇ K as
  • Equation (21) : and h m ' j> , - ⁇ ⁇ m ⁇ ⁇ is the jth-output-to-/eth-error plant impulse response channel .
  • the standard implementation of the filtered-X LMS algorithm also has memory requirements that can exceed the capabilities of a chosen processor.
  • the total storage needed is I J(K + 1 ) L + J K M + Jmax (L, M + 1) + K, and for long controller filter lengths, the bulk of this storage is for the I J K L filtered input signals
  • the preferred embodiment of present invention is a multichannel extension of the new version of the filtered-X LMS algorithm for the single channel control system above.
  • the expression for f a - i , k) ( n — I) is substituted in (22) into the update in
  • Equation OD ⁇ _ ' .(.)( compost_,)- «)( perennial_,. mod).
  • the algorithm employs 2 I " L + J J M + (21 + J) (M - 1) + K MACs per iteration, and it requires I J L + J K M + I L + (T + J + 1)M+ X -l memory locations to implement.
  • this implementation of the multichannel filtered-X LMS adaptive controller modifies the adjoint LMS/CPFE adaptive controller by including the second summation of the RHS of equation (30) and the supporting updates for e m ⁇ j> (n) and r m (n), respectively.
  • the performance difference between the multichannel filtered-X and adjoint LMS/CPFE algorithms can only be expected to be significant for large step sizes. Because the adjoint LMS/CPFE algorithm is a filtered-error technique with an approximate group delay of M samples in the update rule, however, its performance is often worse than that of the filtered-X LMS algorithm. Moreover, the complexity difference between the two algorithms is relatively insignificant for systems with a large number of channels, as will now be shown .
  • each scenario is defined by specific choices of the controller filter length L and plant model filter length M that might be appropriate for a particular type of noise or vibration control task.
  • the quantities RF (C) and R F ⁇ M) denote the ratios of the numbers of MACs and memory locations, respectively, required by the fast implementation with respect to the numbers of MACs and memory locations needed for the original implementation.
  • the corresponding ratios R A (C) and R A (M) are provided for the adjoint LMS/CPFE algorithm with respect to the original filtered-X LMS algorithm.
  • the number of multiples required for the new implementation of the multichannel filtered-X LMS algorithm is less than that of the original algorithm, and this difference is significant for systems with a large number of channels.
  • each input signal is a single sinusoid of a different frequency; thus, each channel of the controller is dedicated to one tonal component of the unwanted acoustic field.
  • Table 3 lists the ratio of MACs and memory locations for the two algorithms with respect to the original filtered-X LMS algorithm in this situation.
  • the new implementation requires only a fraction of the MACs and memory locations used by the original implementation.
  • the new implementation reduces the controller's hardware complexity in narrowband control situations as well.
  • FIG. 2 shows the block diagram of this system, in which ⁇ (k) is the delay-compensated error signal given by
  • Equation (34) r M ⁇ -i
  • This algorithm requires a total of 3L + 2M + 1 MACs per iteration to implement, and it uses 2L + M + max ⁇ L, M + 1 ⁇ + 1 memory locations. Note that this algorithm's performance depends on how well the estimated plant impulse response models the physical response of the plant. As our focus is on implementation and not performance issues, a performance analysis of the multichannel LMS algorithm for active noise control is beyond the scope of this paper.
  • Equation (36) j u _ _, _.
  • Equation ( 39 ) f
  • Equation (42) L > + jJ M
  • Equation (43)
  • Equation ( 6 > : j) (n)r m _ ⁇ -,(n- ⁇ ), and the RHS of (46) can replace the summations of the RIIS of the updates for u m (j> (n) in (39).
  • Equation (47) M - - ⁇ (4/+l) ⁇ r
  • this implementation is more computationally- efficient than the standard implementation in (36).
  • the algorithm in Table 5 is the most-computationally-efficient method out of the three delay-compensation techniques considered when I K ⁇ 7, I K ⁇ 5, and J K ⁇ 8, respectively.
  • this implementation of the multichannel LMS adaptive controller modifies the filtered-X LMS adaptive controller by including the summation within brackets of the RHS of (37) and the supporting updates for u j> (n) . Since u m ' j> (n) is of 0 ( (n)) , the performance difference between the multichannel LMS and filtered-X LMS algorithms can only be expected to be significant for large step sizes. Also note that the filtered-X LMS algorithm is typically derived assuming "slow adaptation, " so that the derivatives of the error signals with respect to the filter coefficients can be easily calculated. Our multichannel LMS algorithms quantitatively define the difference between the filtered-X LMS and LMS coefficient updates and provide an alternative justification for the former algorithm for situations in which the step size is small-valued.
  • the effects that numerical errors due to finite precision calculations have on the performances of the new implementation of the filtered-X LMS and LMS algorithms for active noise control are considered.
  • One important feature of the LMS algorithm in adaptive filtering is its robust behavior in the presence of various approximations and errors that are often introduced in a real-world implementation. Since the original implementation of the filtered-X LMS algorithm and the adjoint LMS/CPFE algorithm are variants of stochastic gradient methods, they share many of the robust convergence properties of the LMS algorithm.
  • the new implementations of the filtered-X LMS and LMS algorithms apply one or more forms of delay compensation to the adjoint LMS/CPFE algorithm. As such, the numerical properties of the delay compensation techniques are of immediate interest, particularly as they affect the long-term performances of the systems.
  • Equation (49) One particularly- useful method, described in more detail in [33], is Equation (49) :

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  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Acoustics & Sound (AREA)
  • Multimedia (AREA)
  • Soundproofing, Sound Blocking, And Sound Damping (AREA)
  • Feedback Control In General (AREA)

Abstract

L'invention concerne un procédé et un appareil destinés à la mise en oeuvre rapide et précise d'un filtre adaptatif à algorithme quadratique moyen minimum à filtration X pour lequel la complexité du système est pondérée conformément au nombre de coefficients de filtrage à l'intérieur du système. Un système de contrôleur mathématiquement équivalent introduit intentionnellement un retard dans le signal de réaction afin de réduire ainsi le nombre de calculs nécessaires pour calculer les coefficients. Le système utilise ensuite la compensation de délais pour compenser les effets du retard, ce qui donne un système qui produit les mêmes résultats qu'un système de contrôleur plus coûteux et plus complexe en termes de calcul.
PCT/US1998/007920 1997-04-18 1998-04-17 Procede et appareil de reduction active multivoie du bruit et des vibrations WO1998048508A2 (fr)

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Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1107225A2 (fr) * 1999-12-01 2001-06-13 Digisonix, Llc Dispositif d'atténuation sonore actif dans lequel le filtre à régression est déterminé par un modèle de test du système global
US7013217B2 (en) 2000-10-16 2006-03-14 Schlumberger Technology Corporation System and method for determining formation slowness
EP1793374A1 (fr) * 2005-12-02 2007-06-06 Nederlandse Organisatie voor Toegepast-Natuuurwetenschappelijk Onderzoek TNO Filtre de réduction active du bruit
CN102496373A (zh) * 2011-12-12 2012-06-13 南京大学 分离式多通道反馈有源噪声控制系统的设计方法
CN109654149A (zh) * 2019-03-01 2019-04-19 武汉轻工大学 基于加速度和力的混合式隔减振器的主动控制方法及系统
CN111722653A (zh) * 2020-07-01 2020-09-29 中国科学院上海技术物理研究所 一种机械制冷机自适应高阶振动主动控制方法

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5613009A (en) * 1992-12-16 1997-03-18 Bridgestone Corporation Method and apparatus for controlling vibration

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5613009A (en) * 1992-12-16 1997-03-18 Bridgestone Corporation Method and apparatus for controlling vibration

Cited By (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1107225A2 (fr) * 1999-12-01 2001-06-13 Digisonix, Llc Dispositif d'atténuation sonore actif dans lequel le filtre à régression est déterminé par un modèle de test du système global
EP1107225A3 (fr) * 1999-12-01 2003-05-02 Digisonix, Llc Dispositif d'atténuation sonore actif dans lequel le filtre à régression est déterminé par un modèle de test du système global
US7013217B2 (en) 2000-10-16 2006-03-14 Schlumberger Technology Corporation System and method for determining formation slowness
EP1793374A1 (fr) * 2005-12-02 2007-06-06 Nederlandse Organisatie voor Toegepast-Natuuurwetenschappelijk Onderzoek TNO Filtre de réduction active du bruit
WO2007064203A1 (fr) * 2005-12-02 2007-06-07 Nederlandse Organisatie Voor Toegepast-Natuurwetenschappelijk Onderzoek Tno Appareil filtre de réduction active de bruit
US8144888B2 (en) 2005-12-02 2012-03-27 Nederlandse Organisatie Voor Toegepastnatuurwetenschappelijk Onderzoek Tno Filter apparatus for actively reducing noise
CN102496373A (zh) * 2011-12-12 2012-06-13 南京大学 分离式多通道反馈有源噪声控制系统的设计方法
CN109654149A (zh) * 2019-03-01 2019-04-19 武汉轻工大学 基于加速度和力的混合式隔减振器的主动控制方法及系统
CN109654149B (zh) * 2019-03-01 2021-07-02 武汉轻工大学 基于加速度和力的混合式隔减振器的主动控制方法及系统
CN111722653A (zh) * 2020-07-01 2020-09-29 中国科学院上海技术物理研究所 一种机械制冷机自适应高阶振动主动控制方法

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