WO2002091353A1 - Systeme et procede antibruit utilisant des modes de rayonnement a large bande - Google Patents

Systeme et procede antibruit utilisant des modes de rayonnement a large bande Download PDF

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Publication number
WO2002091353A1
WO2002091353A1 PCT/NL2002/000297 NL0200297W WO02091353A1 WO 2002091353 A1 WO2002091353 A1 WO 2002091353A1 NL 0200297 W NL0200297 W NL 0200297W WO 02091353 A1 WO02091353 A1 WO 02091353A1
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signals
output signals
sensor output
radiation
controller
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PCT/NL2002/000297
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Arthur Perry Berkhoff
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Nederlandse Organisatie Voor Toegepast-Natuurwetenschappelijk Onderzoek Tno
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Publication of WO2002091353A1 publication Critical patent/WO2002091353A1/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
    • G10K11/1781—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 characterised by the analysis of input or output signals, e.g. frequency range, modes, transfer functions
    • G10K11/17821—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 characterised by the analysis of input or output signals, e.g. frequency range, modes, transfer functions characterised by the analysis of the input signals only
    • G10K11/17825—Error signals
    • 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
    • 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
    • G10K11/1785—Methods, e.g. algorithms; Devices
    • G10K11/17855—Methods, e.g. algorithms; Devices for improving speed or power requirements
    • 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
    • G10K11/17857—Geometric disposition, e.g. placement of microphones
    • 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
    • G10K2210/10—Applications
    • G10K2210/118—Panels, e.g. active sound-absorption panels or noise barriers
    • 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
    • G10K2210/3036—Modes, e.g. vibrational or spatial modes

Definitions

  • the present invention relates to an anti noise system for suppressing primary signals in a space due to a primary source, such as sound radiated from a structure. More particularly the invention relates to a system comprising: - one or more secondary sources to produce secondary signals to suppress the primary signals in the space;
  • controller arranged to: - receive the sensor output signals
  • Active control of sound radiated from structures using structural sensing involves controlling the vibration patterns of the structure that radiate sound efficiently.
  • the methods can be based on the singular value decomposition of the Green's function [1, 2] or an eigenvector analysis of a positive definite radiation operator [3].
  • the resulting vibration patterns are called radiation mode shapes [2, 4].
  • the associated singular values/eigenvalues can be interpreted as radiation efficiencies.
  • Borgiotti [1] noted that the radiation modes are real valued and therefore, in principle, allow delay-free sensing of acoustic radiation. A sensor without delay is particularly important in feedback configurations.
  • a complication for a real-time implementation is that both the radiation mode shapes as well as the radiation efficiencies depend on frequency.
  • a solution was given later by Borgiotti and Jones [5] who demonstrated that minimizing the radiation modal error signals, that are obtained by weighting the sensor signals with the radiation mode shapes at the highest controlled frequency, is sufficient to reduce the sound also at lower frequencies. This is because the radiation modes at a certain frequency form a complete description of the radiating vibration patterns at lower frequencies.
  • a single set of radiation mode shapes is used for all frequencies, although these radiation mode shapes have been obtained for a single frequency (the highest controlled frequency, or, as it will be called in the following the normalization frequency).
  • the so-called normalization frequency [6] the radiation modes do not diagonalize the radiation operator, except for special cases [7]. Therefore, in principle, if the radiation modes at a single normalization frequency are used, all self radiation efficiencies and mutual radiation efficiencies have to be taken into account to be able to compute the exact radiated power at other frequencies. Simplifications were given [8, 9], demonstrating that good sound power reductions can be obtained by using only the self radiation efficiencies. It was also shown that the choice of the radiation mode shapes is not critical, provided they form a complete set of basis functions for the radiating vibration patterns in the frequency range of interest [9]. In some cases, such as for free-field sound radiation, frequency dependent weighting might not be strictly necessary [9]. In other cases, however, a frequency dependent weighting of the radiation modal error signals was found to be necessary, especially in enclosed spaces [10]. There seems to be agreement that frequency independent spatial filters can, in general, be used for broadband active noise control problems involving sound radiation from plates.
  • an anti noise system that provides improved anti noise control in practical situations, e.g. situations where vibrating bodies do not have a theoretically simple shape or are present in enclosed volumes of complex form and materials.
  • an anti noise system according to the invention as defined in the preamble is characterized in that the controller is also arranged to - calculate the error signals by weighting the sensor output signals with radiation mode shapes determined for a plurality of frequencies in a predetermined frequency band.
  • the invention addresses the determination of the radiation mode shapes and associated efficiencies based on broadband sound radiation.
  • the system does not determine the radiation mode shapes for transfer characteristics obtained from measurements for a single normalization frequency.
  • the system uses determines the radiation mode shapes for what is effectively a frequency averaged transfer characteristic. As shown in appendix A, this ensures a complete set of modes.
  • the radiation modes obtained in this way are the optimum vibration patterns in an average sense evaluated over a predefined frequency band. This eliminates the need for selection of a normalization frequency.
  • the weighting schemes for the actuator array are optimized in a broadband sense for coupling to the acoustic field at low frequencies, while being constrained by a reduced coupling to the acoustic field at high frequencies. This minimizes the 'spillover' effect [12], which can lead to undesirable increases in sound power of the high frequency components if the low 30 frequency components are reduced.
  • Modal sensors and modal actuators based on spatially continuous transducers were discussed by Lee and Moon [13].
  • the invention is preferably based on discrete sensors and actuators, such as described by Gawronski [14] and Morgan [15], in order to provide more flexibility by using programmable weighting coefficients.
  • the emphasis in the present invention is on acoustic radiation and the connection with previous radiation mode theory.
  • the present invention also relates to an anti noise method for suppressing primary signals in a space due to a primary source, comprising the steps of:
  • the invention relates to a computer program product to be loaded by an anti noise system for suppressing primary signals in a space due to a primary source, the system comprising:
  • the present invention relates to a data carrier provided with a computer program product, as defined above.
  • the invention also relates to a method for identification of multiple radiation modes from experimental data by using further sensors, e.g., microphones, in the far field, the far field being defined as comprising those locations which are further away from the secondary sources than the longest wave length of interest.
  • the present invention provides a method of calibrating an anti noise system as defined above, comprising the steps of:
  • the calibration can also be done in an alternative way.
  • the invention also relates to a method of calibrating an anti noise system as defined above, comprising the steps of:
  • the invention also relates to a method of calibrating an anti noise system as defined above, comprising the steps of:
  • Figure 1 shows a transfer function from actuator current to far field pressure
  • Figures 2a, 2b, 2c, 2d show the radiation mode shapes
  • Figure 3 shows eigenvalues obtained with a time domain technique
  • Figures 4a, 4b, 4c, 4d show radiation mode shapes
  • Figure 5 shows eigenvalues obtained with a frequency domain technique
  • Figures 6a, 6b, 6c, 6d show radiation mode shapes
  • Figure 7 shows eigenvalues
  • Figures 8a, 8b, 8c, 8d show radiation mode shapes
  • Figure 9 shows eigenvalues obtained with the reconstructed Green's function.
  • Figure 10 shows a schematic diagram of an active feedback control system
  • Figure 11a shows a configuration for calibration of the system
  • Figure lib shows a configuration for the reduction of sound
  • Figure 12 shows an actuator configuration and a sensor configuration
  • Figure 13 shows the sound transmitted with and without feedback control
  • Figure lib shows a configuration for the reduction of sound transmitted through a plate by using weighting schemes for actuators and sensors.
  • a primary sound field is due to a source 2 which produces primary vibrations of a structure la, lb.
  • the primary source (2) as indicated in Figure lib is an acoustic source, the actual primary source can also be a mechanical primary source which directly excites the structure.
  • Figure lib shows an object or structure la, lb e.g., a plate (that may have an arbitrary shape and may be located in an enclosure), that is made to vibrate by means of a plurality of actuators 3a.
  • the actuators 3a may be piezoelectric transducers or shakers driven by a driving signal u.
  • Object 1 also contains a plurality of sensors 3b.
  • the sensors 3b consist of piezoelectric transducers and may be combined with the actuators 3a into the same physical transducers.
  • Each of the sensors 3b produce an output signal corresponding with quantity q (e.g. velocity or pressure or strain).
  • the output signals q are received by a controller 5.
  • the controller 5 comprises means for multiplying the output signals q by the radiation modes E. The resulting signals are summed to render error signals v.
  • Block 11 denotes that the controller 5 is arranged with means to (optionally) perform a frequency dependent weighting operation K on error signals v to provide resulting error signals e (equation (20)).
  • the resulting error signals e are used by the controller 5 to control adaptive parameters of an adaptive controller 13.
  • Adaptive controller 13 produces output signals applied to a filter 15 with fixed filter coefficients W.
  • Filter 15 produces actuator drive signals u. These actuator drive signals u are optionally amplified.
  • the controller 5 has been shown in a very schematic way to clearly demonstrate the different signals of the calculations presented here.
  • the blocks shown in controller 5 need not be physically present. There may be just one processor performing all the necessary calculations and simulating the block scheme of figure lib .
  • the controller may be designed with different parallel operating processors or with processors in a master-slave configuration, as is known to persons skilled in the art. Basically, there is no restriction as to how the controller is designed as long as it is capable of performing the essential features of the annexed claims. Even analoque and/or digital circuits can be used, as the case may be.
  • Figure 11a shows a configuration for calibration of the system, that is the determination of coefficients involved in the weighting operation K, the filter coefficients W, W" and/or the radiation modes E.
  • the calibration procedure uses excitation of the structure 1 and the simultaneous measurement of the sensor output signals q and the corresponding far field pressure signals p.
  • the radiation modes E are identified in situ.
  • the method of identifying the radiation modes is based on the excitation of the structure with a number of different excitation patterns and acquisition of the resulting structural sensor signals q and far field pressure signals p with the configuration shown in Figure 11a.
  • a time-domain inverse filtering technique is used to extract an underlying Green's function, which gives the response in the far field in terms of elementary sources on the structure.
  • the time domain technique has the advantage that a single minimization procedure is used to obtain the complete impulse response.
  • the acoustic power radiated from a vibrating structure to the far field can be derived from measurement of the time-averaged squared sound pressure at a relatively large distance from the structure using a sufficient number of measurement positions [16].
  • Global sound pressure reduction inside an enclosure is related to the reduction of the potential energy in the enclosure, which can be estimated from the squared sound pressure at a number of positions (N) evenly distributed over the interior of the enclosure.
  • the cost function can be expressed as:
  • the M M dimensional matrix P GG ( ⁇ ) contains information about the vibration patterns of q( ⁇ ) that are significant to p( ⁇ ) . These vibration patterns can be obtained by an eigenvector analysis of P GG ( ⁇ ) , which is a well- known procedure ([19], p.72). In the limit for an infinite number of pressure sensors at an infinite distance from the radiator, assuming that q( ⁇ ) represents a velocity vector, the matrix P GG ( ⁇ ) approaches the matrix R( ⁇ ) of Elliott and Johnson [4] up to a scaling factor.
  • the matrix E contains the broadband radiation mode shapes and the diagonal matrix ⁇ contains the broadband radiation efficiencies. Since PGG(0) is symmetric, positive definite and real, the eigenvalues are also real.
  • the matrices E and ⁇ are truncated to retain only the most significant, principal, components. In theory, the radiation modes obtained from the integral of P GG ( ⁇ ) over ⁇ are identical to that obtained from
  • the eigenvectors in E are not completely orthogonal for acoustic radiation at each frequency but only approximately. They are however usable for broadband sound radiation control in the same sense as the radiation modes at the highestcontrolled frequency, as suggested for free space radiation by Borgiotti and Jones [5].
  • the essential observation to be made is that, because the radiation modes at a certain highest frequency are a complete set of basis functions for acoustic radiation at all lower frequencies, then also the eigenvectors obtained from an averaging procedure over frequency up to this highest frequency, that lead to Eq. (17), are a complete set of basis functions.
  • a proof is given in the appendix.
  • the resulting eigenvectors are not radiating independently, and consequently are not modes in a strict sense, they are called broadband radiation modes because of the close correspondence with the frequency domain radiation modes.
  • Broadband radiation modes also provide an unambiguous solution to the selection of a set of basis functions in enclosed spaces. In enclosed spaces, Borgiotti and Jones' suggestion does not always give the best results because of the strong frequency dependence of the radiation modes. If broadband radiation modes are used then automatically the modes are selected which are optimum for the frequency range of interest, because all frequency dependent radiation properties are taken into account. However, these modes are optimum in an average sense and a subsequent frequency dependent weighting may be required. Another property of the time domain technique is that the resulting radiation modes are real valued. For positive definite radiation operators, this also holds for frequency domain techniques but in practice, using measured data from a finite number of field sensors at a finite distance, these radiation modes are not entirely real.
  • the formulation of the previous section can be used for the identification of the radiation modes E in situ.
  • the method is based on the excitation of the structure with a number of different excitation patterns and acquisition of the resulting structural sensor signals q and far field pressure signals p.
  • the configuration is shown in Figure 11a.
  • a time-domain inverse filtering technique is used to extract the underlying Green's function, which gives the response in the far field in terms of elementary sources on the structure.
  • the time domain technique has the advantage that a single minimization procedure is used to obtain the complete impulse response. Instead, for the frequency domain technique, the impulse response has to be assembled from partial optimization results, each using a limited information content.
  • ⁇ a weighting ' coefficient for the Green's function coefficients.
  • a frequency dependent weighting can be applied that corresponds to the frequency range for which the radiation modes have to be determined.
  • the different excitation patterns k could also be applied simultaneously, leading to an improved signal to noise ratio.
  • an adaptive algorithm such as a least-mean-square algorithm, to search for the coefficients of the Green's function. If the Green's function contains strongly resonating behavior, such as in an enclosed space, then it may be advantageous to combine information regarding the poles of the system, such as with a state-space description [25].
  • A denotes the situation in which the source is at position x m and the receiver is at position x n
  • B denotes the situation in which the source is at position x n and the receiver is at position x m
  • A is the direct method
  • the advantage of the reciprocal technique is that much larger sources can be used for measuring the transfer functions and that the responses can be obtained almost directly at the radiating surface. It is noted that the reciprocal technique can be used equally well for measuring radiation modes in enclosed spaces, which in this case are the velocity patterns that contribute to the potential energy in the enclosure.
  • Subsection 2.1 a method was given to obtain radiation modes after excitation of the structure with different excitation patterns and the acquisition of the resulting structural sensor signals and far field pressure signals.
  • the available actuators can often be used to generate the excitation patterns for plate vibration in order to extract the radiation modes.
  • two types of transfer functions are required: the transfer from actuator drive signal to structural sensor and the transfer from actuator drive signal to far field sensor. Measurement of the first type of transfer function usually gives no problems. However, measurement of the second type of transfer functions can be troublesome due to large background noise, especially if the actuators are relatively small. In such cases it can be better to use a reciprocal technique for measuring the transfer from actuator drive signal to the far field signal, which is obtained by using the actuator as sensor.
  • e is the voltage on the actuator
  • q is the volume velocity of an acoustic source
  • p is the pressure in the field
  • i is the current going through the actuator.
  • A denotes the situation in which actuator k is driven by a current source i and in which the resulting pressure p at far field position x is measured
  • B denotes the situation in which a source of volume velocity q at far field position x is used and in which the resulting voltage e at actuator k is measured.
  • coordinate x corresponds to far field position n, as used previously. That Eq. (30) is valid in a large frequency range can be seen in Figure 1. Larger differences can be found at low frequencies but this is the region where the direct method suffers from noise. The curves from the reciprocal method behave as expected, also at low frequencies.
  • the broadband radiation mode formulation can also be used for the design of signal processing schemes that drive an array of actuators.
  • a control scheme as shown in figure lib can advantageously be used in a broadband scheme according to the invention.
  • Figure lib shows an object la, lb e.g., a plate (that may have an arbitrary shape and may be located in an enclosure), that is made to vibrate by means of a plurality of actuators 3a.
  • the primary sound field is due to a source (2) which produces primary vibrations of the structure.
  • the primary source (2) as indicated in Figure lib is an acoustic source, the actual primary source can also be a mechanical primary source which directly excites the structure.
  • the actuators 3a may be piezo-electric transducers or shakers driven by a driving signal u.
  • Object 1 also contains a plurality of sensors 3b.
  • the sensors 3b consist of piezoelectric transducers and may be combined with the actuators 3a into the same physical transducers.
  • Each of the sensors 3b produce an output signal corresponding with quantity q (e.g. velocity or pressure or strain).
  • the output signals q are received by a controller 5.
  • the controller 5 comprises means for multiplying the output signals q by the radiation modes E.
  • the resulting signals are summed to render error signals v, in accordance with Eq. (18).
  • Block 11 denotes that the controller 5 is arranged with means to (optionally) perform a frequency dependent weighting operation K on error signals v to provide resulting error signals e (equation (20)).
  • the resulting error signals e are used by the controller 5 to control adaptive parameters of an adaptive controller 13.
  • Adaptive controller 13 produces output signals applied to a filter 15 with fixed filter coefficients W.
  • Filter 15 produces actuator drive signals u. These actuator drive signals u are optionally amplified.
  • the controller 5 has been shown in a very schematic way to clearly demonstrate the different signals of the calculations presented here.
  • the blocks shown in controller 5 need not be physically present. There may be just one processor performing all the necessary calculations and simulating the block scheme of figure lib .
  • the controller may be designed with different parallel operating processors or with processors in a master-slave configuration, as is known to persons skilled in the art. Basically, there is no restriction as to how the controller is designed as long as it is capable of performing the essential features of the annexed claims. Even analoque and/or digital circuits can be used, as the case may be.
  • the actuator scheme is required to consist of a set of nearly independent driving patterns, the so-called actuator modes, that have good sensitivity for sound radiation in the frequency range where sound power reductions have to be obtained. This frequency range is usually the low frequency range.
  • the actuator configuration is preferably designed in such a way that, in the frequency range where the nearfield sensor configuration fails to predict the farfield sound field, usually in the high frequency range, the actuator modes have a small sensitivity for sound radiation.
  • the configuration is preferably designed in such a way that it has a minimum of 'spillover'. In the following a method is given to statisfy these requirements using a given physical actuator configuration.
  • the present formulation optimizes a signal processing scheme for a given actuator array.
  • the advantage is that the system can be calibrated in-situ with measured transfer functions using an identical actuator array which can be used for different situations.
  • One approach is a technique to minimize the modal contributions due to the secondary path which are not taken into account by error sensors.
  • the secondary path is the path followed by the signals produced by the actuators to the error sensors.
  • the present description gives an extension to broadband signals and an optimization for acoustic radiation and not simply mechanical vibration.
  • Still a further extension is that a systematic method is presented to reduce spillover at high frequencies by defining two different sets of vibration patterns, one set of which is used for good sound power reductions at low frequencies, while the other set is used for the reduction of spillover.
  • matrix W(t) is represented in figure lib by both the adaptive controller 13 (W") and the filter W with fixed coefficients W'k m . Further, let q s (t) be the vector of secondary signals at the sensors
  • H(t) the matrix of transfer functions of the secondary path from actuator signal vector to sensor signal vector, as in
  • the radiation mode sensor signal vector for the observed radiation modes in E due to the secondary sources (i.e. the actuators 3a) is
  • the total error signal vector is simply the sum of a primary signal vector (i.e. a vector related to a primary disturbance source) and the secondary signal vector given by
  • the radiation modal sensor signal vector due to the secondary sources (i.e. the actuators 3a) for a selected set of unobserved radiation modes E' is
  • Figure 10 shows a possible configuration for a feedback controller.
  • the contribution of the secondary path on the reference signal x is subtracted in the controller, which leads to an input signal on the controller W which only consists of the primary signal Vd. This is accomplished by subtracting from the measured signal v the secondary path signal v s .
  • the input signal to the controller is unrelated to the secondary signals and consists only of the primary signal Vd.
  • the configuration can be regarded as feedforward and the design techniques of feedforward control systems apply.
  • the preconditioner can be computed off-line.
  • a possible practical implementation of such a scheme with a preconditioner W and an adaptive controller W" is shown in Figure lib.
  • the filter W can be obtained in an iterative way where the various error signals and constraints are taken into account in the iteration scheme.
  • a method to obtain E is by low -pass filtering of the Green's functions if reductions at low frequencies have to be obtained.
  • the constraint modes E' can not be obtained from the same technique. This is due to the fact that the modes in E' should be the modes that are efficient radiators at high frequencies only. Therefore, a low pass filtering operation of the Greens' functions would eliminate these components, which is undesirable. Also a high-pass filtering of the Green's function is inadequate because the resulting radiation modes are not only efficient radiators at high frequencies, but also possibly efficient radiators at low frequencies.
  • the modes E' that are the most efficient radiators in a broadband sense under the constraint that they are orthogonal to the modes E which have previously been found as the most efficient radiators at low frequencies. This implies that the modes E' are efficient radiators at high frequencies and inefficient radiators at low frequencies. Hence, the modes E' can be used as constraint vectors in order to optimize the actuator configuration.
  • the vectors in the columns of E' are the most significant modes in PGG(0) under the condition that they are orthogonal to the column vectors in E.
  • t denotes continuous time
  • p is the density of air
  • Sm is the area of a so-called elemental radiator [4]
  • ⁇ is a temporal Dirac impulse function
  • c 343 m/s is the speed of sound
  • r mn ⁇ ⁇ m - is the distance between source coordinate Xm. and receiver coordinate x n .
  • Discrete-time representations gmn(t) were obtained by linear interpolation, using samples of Eq. (48). Source points were assumed to be distributed over a rectangular area of 60 cm x 75 cm, using 5 x 6 sources.
  • the pressure was recorded at 12 positions on a hemisphere with a radius of 5 m according to the AS1217.6-1985 standard, as described in [30].
  • the low-pass filter and the differentiator were implemented with 21-tap and 11-tap FIR filters, respectively.
  • the first four resulting radiation modes are shown in Figures 2a, 2b, 2c, 2d, and the thirty normalized eigenvalues in Figure 3.
  • the time domain result and the averaged frequency domain result are nearly equal, as expected.
  • the eigenvalues are nearly equal.
  • the method of Section 2 was used to estimate the time domain Green's function G(t) and the resulting broadband radiation modes E.
  • the discrete-time Green's function corresponding to Eq. (48) was estimated by exciting a plate with 30 piezoelectric patch actuators [12]. For each actuator, the resulting velocities at 30 positions on the plate were recorded as well as the pressure at 12 positions in the far field of the plate. For the velocity and pressure sensors, the same positions were used as in Subsection 4.1.
  • the value of ⁇ was set to such a value that the relative mean- squared contribution of ⁇ ⁇ ⁇ g ⁇ ( ⁇ )g n ( ⁇ ) to the diagonal of the matrix resulting from EJ[ ejj (t)] 2 ⁇ was equal to 10" 4 .
  • a simply supported aluminium sandwich plate of 6 mm thickness was used. The width and height were 60 cm and 75 cm, respectively.
  • the number of plate modes taken into account was 8 x 8.
  • the Greens function coefficients were collected in a 30 x 12 matrix of FIR filters having 32 samples each, using a sampling frequency of 1 kHz.
  • the resulting first four radiation modes are shown in Figures 8a-8d and the corresponding eigenvalues in Figure 9. It can be seen that the shapes of the first three modes ( Figures 8a-8c) are similar to the corresponding shapes in Figure 2.
  • the shape of the fourth mode in Figure 8d is different from the one in Figure 2d. This can be explained by looking at the eigenvalues in Figure 9. It can be seen that the fourth-order eigenvalue and other high-order eigenvalues have a much lower value than the first three eigenvalues, and therefore are relatively unimportant. Errors due to the reconstruction process can lead to changes from the theoretical results, especially for the small eigenvalues. However, small reconstruction errors should not have a significant effect on large eigenvalues, as can be seen in the results. This was supported by other numerical experiments.
  • the modes E were obtained by low-pass filtering the Greens' function at 288 Hz, computing the eigenvectors of the transfer correlation matrix, and using the three strongest modes.
  • the constraint modes E' were obtained by an eigenvector computation based on the unfiltered Green's function under the constraint that they had to be orthogonal to the three modes in E, as described in Subsection 3.2.
  • the parameters of the plate were the same as in the previous example.
  • An analytical method for the computation of weighting coefficients for the piezoelectric sensor array was used, as described previously [31].
  • the control configuration was based on Internal Model Control [32], where the contribution v s of the secondary path on the detection signal vector was subtracted from the measured signal vector v in the controller ( Figure 10). In this way the controller coefficients W and the resulting performance of the system could be computed by using the techniques for feedforward control.
  • the configuration was a feedback system where the reference signals x(t) were equal to the unfiltered radiation modal error signals vd(t), and where the signals ⁇ (t) and s(t) were obtained by a frequency dependent filtering of the radiation modal error signals, by using the diagonal of matrix K(t).
  • the frequency dependency was implemented by a least-squares fit of the frequency dependent efficiency of the radiation modes, using the Matlab function firls.
  • the order of the filters was chosen to be 10.
  • a controller delay of 1 sample was assumed.
  • the radiated sound power was evaluated by computing the plate velocity before control and after control at 10 x 10 positions.
  • the influence on the performance of each of the individual parameters Bi, B2 and ⁇ was investigated. For each of these parameters, a value could be found for which the reduction of the broadband radiated sound power was maximum. The results which are shown are at these maximum values of reduction. The results are given in Figure 13.
  • the broadband reductions for coefficient weighting with 6 ⁇ , effort weighting with ⁇ 2 , and radiation modal constraint weighting with Qs are 8.0 dB, 6.7 dB, and 9.9 dB, respectively.
  • the performance with modal constraint weighting is better than with the other two methods.
  • the results substantially degrade for weighting with Bi or Q2, while being relatively close to the above result for weighting with ⁇ 3 -
  • the performance depended less critically on the actual value of ⁇ 3 than on & ⁇ or ⁇ 2 .
  • the result for modal constraint weighting is the only result which does not lead to increases at any frequency. According to an approximate formula [9], the maximum frequency for which significant reductions can be obtained using 3 radiation modes for a plate of 60 cm x 75 cm is approximately 300 Hz, which agrees with the results of Figure 13.
  • the cost function J " was also minimized for each of the radiation modal error signals independently.
  • the constraint modes were augmented with the remaining radiation modes, which are two modes in this case.
  • the results were similar to the previous results with slightly smaller reductions, being 7.6 dB, 6.7 dB and 8.5 dB, for weighting with Bi, Q2 and ⁇ 3 , respectively.
  • the advantage is that the systems obtained in this way are more robust than those obtained from the simultaneous minimization of the radiation modal error signals.
  • the quantification of robustness was based on a method described by Elliott [33].
  • the maximum singular value of 30 the open-loop gain at any frequency was 700 for the simultaneous optimization and approximately 20 for the independent minimization. It is noted that the latter configuration is a true modal actuator, and therefore the adaptive filter could be chosen to be diagonal. In other words, each radiation modal error signal could be controlled independently by the corresponding radiation modal actuator.
  • the simultaneous minimization procedure leads to a fully coupled controller, i.e., secondary signals are generated on all radiation modal error sensors for each radiation modal reference signal.
  • the additional freedom allowed in the simultaneous minimization procedure is used by the algorithm to create a fully coupled controller in order to be able to fulfill to a further extent the concurring requirements imposed on radiation modal error signals and contribution of the secondary path on the constraint modes.
  • the number of actuators is larger than the number of error signals. Also for the case where the number of actuators was less than or equal to the number of error signals the performance of the modal weighting scheme was found to give the largest reduction of broadband radiated sound power. However, for that case the differences were smaller, especially between effort weighting and modal constraint weighting.
  • FIR filters finite impulse response filters were assumed for the Green's function G, for the secondary path H, for the frequency dependent weighting matrix K, and for the controllers W, W, W". It is noted that the methods as described in the present invention are not limited to FIR filters but can be based on other models, such as Infinite Impulse Response (IIR) filters, state-space implementations, or still other implementations. It is also noted that other control strategies are possible than Internal Model Control, which was used in the examples.
  • IIR Infinite Impulse Response
  • the techniques of the present invention give extensions for: higher order radiation modes (i.e. reductions also for ka > 1), a method for the design of modal actuators, the reduction of controller dimensionality, a method to limit undesired sound power increases at high frequencies, and a suggested technique to obtain radiation modes in situ.
  • the broadband radiation modes were used to obtain driving schemes for a configuration consisting of arrays of piezoelectric sensors and piezoelectric actuators.
  • Three methods for the derivation of the driving schemes were compared. It has been shown that an optimum filter based on constraints on a special set of vibration patterns, of which the outputs were weighted with frequency dependent filters, gave better results than that obtained with coefficient weighting and control effort weighting. These constraint patterns were computed in such a way that they were inefficient radiators at low frequencies and efficient radiators at high frequencies.
  • the new weighting scheme was found to be less sensitive to changes in the configuration. Also the choice of the weighting parameter was less critical. In this way efficient modal sensors and modal actuators can be designed having a good tradeoff between large sound power reductions in the controlled frequency range and a minimum of increased sound power in the uncontrolled frequency range.
  • range Rk c range Rk+i (nesting property), (A3)
  • range R range R#, (A4) which is the desired result, because range RK provides a complete set of basis functions for the reduction of sound radiation for all frequencies below QK.
  • the eigenvectors of R that are efficient radiators at low frequencies are efficient radiators also at high frequencies. Therefore these eigenvectors are weighted more heavily, i.e. have larger eigenvalues, than the eigenvectors of R that are efficient radiators mainly at high frequencies.

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

Abstract

Cette invention concerne un système et un procédé antibruit visant en particulier à supprimer le son rayonné par une structure, au moyen d'une formule des diagrammes vibratoires rayonnant le plus efficacement possible d'un corps vibrant, les modes de rayonnement, dans le domaine temporel. Les modes de rayonnement peuvent être utilisés pour obtenir des systèmes de pondération efficaces pour un réseau de capteurs afin de réduire la dimensionnalité de l'unité de commande. Les modes de rayonnement particuliers sont déterminés sur la base de signaux à large bande. Un procédé est utilisé pour obtenir ces modes à partir de signaux pouvant être mesurés sur des capteurs dans le champ proche et des microphones dans le champ éloigné. Les modes de rayonnement à large bande sont utilisés pour la conception d'un réseau d'actionneurs dans un système de commande à rétroaction afin de réduire la puissance acoustique rayonnée par un objet. Trois procédés différents de conception de l'actionneur sont comparés, tenant compte de la réduction de la puissance acoustique rayonnée dans la gamme de fréquences contrôlée, mais également d'une éventuelle augmentation de la puissance acoustique rayonnée dans une gamme de fréquences non contrôlée.
PCT/NL2002/000297 2001-05-07 2002-05-06 Systeme et procede antibruit utilisant des modes de rayonnement a large bande WO2002091353A1 (fr)

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Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106556459A (zh) * 2015-09-25 2017-04-05 中国科学院声学研究所 一种用于低频声源测试的双端面的力声互易装置和方法
CN106556459B (zh) * 2015-09-25 2023-06-20 中国科学院声学研究所 一种用于低频声源测试的双端面的力声互易装置和方法
EP3435372A1 (fr) * 2017-07-28 2019-01-30 Harman Becker Automotive Systems GmbH Génération de zone silencieuse
KR20190013568A (ko) * 2017-07-28 2019-02-11 하만 베커 오토모티브 시스템즈 게엠베하 무성역 생성
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KR102448107B1 (ko) 2017-07-28 2022-09-27 하만 베커 오토모티브 시스템즈 게엠베하 무성역 생성
CN114170992A (zh) * 2022-02-11 2022-03-11 科大讯飞(苏州)科技有限公司 一种车辆主动降噪效果评价方法、装置、存储介质及设备
CN114170992B (zh) * 2022-02-11 2022-08-05 科大讯飞(苏州)科技有限公司 一种车辆主动降噪效果评价方法、装置、存储介质及设备

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