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An optimal local active noise control method based on stochastic finite element models
Abstract
A new method is presented to obtain a local active noise control that is optimal in stochastic environment. The method uses numerical acoustical modeling that is performed in the frequency domain by using a sequence of finite element discretizations of the Helmholtz equation. The stochasticity of domain geometry and primary noise source is considered. Reference signals from an array of microphones are mapped to secondary loudspeakers, by an off-line optimized linear mapping. The frequency dependent linear mapping is optimized to minimize the expected value of error in a quiet zone, which is approximated by the numerical model and can be interpreted as a stochastic virtual microphone. A least squares formulation leads to a quadratic optimization problem. The presented active noise control method gives robust and efficient noise attenuation, which is demonstrated by a numerical study in a passenger car cabin. The numerical results demonstrate that a significant, stable local noise attenuation of 20–32 dB can be obtained at lower frequencies (< 500 Hz) by two microphones, and 8–36 dB attenuation at frequencies up to 1000 Hz, when 8 microphones are used.
... A local noise reduction of 20-32 dB on the driver's ears has been obtained. 10 Cheer and Eliot also devised a multichannel ANC system for a car by considering the uncertainties caused by inaccuracy in modeling and changing the number of occupants. The overall design of the controller could minimize the sum of the squares of the microphone error signals with such constraints as robust stability, the limitation of the increased sound level, and open-loop controller stability. ...
... The amounts of absorption coefficients of each panel have been extracted from a previous study. 10 There is at least one driver in the car, and it is likely that there are four occupants. The presence of these occupants and their movements might change the frequency response of sound pressure at the occupants' ears. ...
... Thickness, module of elasticity and sound absorption coefficient for structural panels.10 ...
The sound level inside an automobile cabin plays a major role in the passengers’ comfort. Active noise control has been widely used to reduce the sound level inside the car cabin. This article presents a design of an active and robust sound control system that can still be efficient despite the changes inside the passengers’ compartment caused by the movement of the occupants. Initially, the coupled acoustic structural analysis is done on a simplified model of an automobile cabin by using finite element and modal coupling methods. Then, the uncertainty of the sound field inside the car, due to the presence of the occupants and the displacement of their heads, is investigated. A multi input multi output robust feedback control strategy, using the H∞ method and considering the unstructured uncertainty of the acoustic structural system, is proposed to reduce the sound pressure level at the ears of all the occupants. In order to achieve performance targets in a broad bandwidth and to reduce the waterbed effect, an optimization is performed on the weight function coefficients. The results show that in the frequency range of 0–334 Hz, the controller has an acceptable performance which is robust to changes in the interior sound field.
... Kwon and Park propose an active window system, which uses a feedforward control method for active noise control, to reduce the exterior noise sources, such as traffic noise and construction noise which enter rooms through open windows used for natural ventilation [19]. Airaksinen and Toivanen present a new method by using numerical acoustical modeling to obtain a local active noise control that is optimal in stochastic environment [20]. Tanaka deals with local as well as global ANC using a parametric array loudspeaker (PAL) possessing intriguing properties: sharp directivity, low sound pressure decay by distance, and capability of steering directivity [21]. ...
... In an open inverted cone space with the V2.0 device set at its vertex, we address the following aspects for analysis: (1) the general effect on the noise reduction of this V2.0 device; (2) the impacts of the different frequencies on the noise reduction effect; (3) the impacts of ⋅ (0, 25)). In order to simulate the inverted cone space, the other three points including (10,5), (20,10), and (30,15) are added in this testing. According to the axis-symmetric principle, we use the test results of the three test points instead of the test results of conical surface. ...
Noise pollution has been given more attention due to its negative impacts on human health and disease. The portable low-frequency noise reduction device we developed in this research can provide an effective way for solving low-frequency noise pollution problem in the small space. This work describes the design principle and the prototype structures for two versions of V1.5 and V2.0 and builds the noise test systems for small spaces, respectively. These devices, installed on the outer surface of the small spaces, can automatically identify the noise spectrum and implement noise reduction by means of the active noise control (ANC) technology. The testing results indicate that the noise can be reduced 12 dB in the range of 250 Hz~400 Hz for the small closed space while, for the small open space, the best effect of 5.88 dB occurs in the optimal frequency of 450 Hz. These effects will be weakened with the increasing distance away from the source and show the obvious axisymmetric distribution in the inverted cone space.
A numerical method for optimizing the local control of sound in a stochastic domain is developed. A three-dimensional enclosed acoustic space, for example, a cabin with acoustic actuators in given locations is modeled using the nite element method in the frequency domain. The optimal local noise control signals minimizing the least square of the pres-sure eld in the silent region are given by the solution of a quadratic opti-mization problem. The developed method computes a robust local noise control in the presence of randomly varying parameters such as variations in the acoustic space. Numerical examples consider the noise experienced by a vehicle driver with a varying posture. In a model problem, a signi-cant noise reduction is demonstrated at lower frequencies.
State-of-the-art finite-element methods for time-harmonic acoustics governed by the Helmholtz equation are reviewed. Four major current challenges in the field are specifically addressed: the effective treatment of acoustic scattering in unbounded domains, including local and nonlocal absorbing boundary conditions, infinite elements, and absorbing layers; numerical dispersion errors that arise in the approximation of short unresolved waves, polluting resolved scales, and requiring a large computational effort; efficient algebraic equation solving methods for the resulting complex-symmetric non-Hermitian matrix systems including sparse iterative and domain decomposition methods; and a posteriori error estimates for the Helmholtz operator required for adaptive methods. Mesh resolution to control phase error and bound dispersion or pollution errors measured in global norms for large wave numbers in finite-element methods are described. Stabilized, multiscale, and other wave-based discretization methods developed to reduce this error are reviewed. A review of finite-element methods for acoustic inverse problems and shape optimization is also given. © 2006 Acoustical Society of America.
We present an efficient method for the numerical realization of elliptic PDEs in domains depending on random variables. Domains
are bounded, and have finite fluctuations. The key feature is the combination of a fictitious domain approach and a polynomial
chaos expansion. The PDE is solved in a larger, fixed domain (the fictitious domain), with the original boundary condition
enforced via a Lagrange multiplier acting on a random manifold inside the new domain. A (generalized) Wiener expansion is
invoked to convert such a stochastic problem into a deterministic one, depending on an extra set of real variables (the stochastic
variables). Discretization is accomplished by standard mixed finite elements in the physical variables and a Galerkin projection
method with numerical integration (which coincides with a collocation scheme) in the stochastic variables. A stability and
convergence analysis of the method, as well as numerical results, are provided. The convergence is “spectral” in the polynomial
chaos order, in any subdomain which does not contain the random boundaries.
Physical phenomena in domains with rough boundaries play an important role in a variety of applications. Often the topology of such boundaries cannot be accurately described in all of its relevant detail due to either insufficient data or measurement errors or both. This topological uncertainty can be efficiently handled by treating rough boundaries as random fields, so that an underlying physical phenomenon is described by deterministic or stochastic differential equations in random domains. To deal with this class of problems, we propose a novel computational framework, which is based on using stochastic mappings to transform the original deterministic/stochastic problem in a random domain into a stochastic problem in a deterministic domain. The latter problem has been studied more extensively, and existing analytical/numerical techniques can be readily applied. In this paper, we employ both a stochastic Galerkin method and Monte Carlo simulations to solve the transformed stochastic problem. We demonstrate our approach by applying it to an elliptic problem in single- and double-connected random domains, and comment on the accuracy and convergence of the numerical methods.
The active control of sound is analyzed in the framework of the mathematical theory of optimal control. After setting the problem in the frequency domain, we deal with the state equation, which is a Helmholtz partial differential equation. We show existence of a unique solution and analyze a finite element approximation when the source term is a Dirac delta measure. Two optimization problems are successively considered. The first one concerns the choice of phases and amplitudes of the actuators to minimize the noise at the sensors location. The second one consists in determining the optimal actuators placement. Both problems are then numerically solved. Error estimates are settled and numerical results for some tests are reported. Key words. Dissipative acoustics, noise reduction, active control, optimal control problem, finite element approximation. AMS subject classifications. 49J20, 49K20, 65N15 1. Introduction. Noise
An active feedforward control system has been developed to reduce the road booming noise that has strong nonlinear characteristics. Four acceleration transducers were attached to the suspension system to detect reference vibration and two loudspeakers were used to attenuate the noise near the headrests of two front seats. A leaky constraint multiple filtered-X LMS algorithm with an IIR-based filter that has fast convergence speed and frequency selective controllability was proposed to increase the control efficiency in computing power and memory usage. During the test drive on the rough asphalt and turtle-back road at a constant speed of 60 km/h, we were able to achieve a reduction of around 6 dB of A-weighted sound pressure level in the road booming noise range with the proposed algorithm, which could not be obtained with the conventional multiple filtered-X LMS algorithm.
Active noise control exploits the long wavelengths associated with low frequency sound. It works on the principle of destructive interference between the sound fields generated by the original primary sound source and that due to other secondary sources, acoustic outputs of which can be controlled. The acoustic objectives of different active noise control systems and the electrical control methodologies that are used to achieve these objectives are examined. The importance of having a clear understanding of the principles behind both the acoustics and the electrical control in order to appreciate the advantages and limitations of active noise control is emphasized. A brief discussion of the physical basis of active sound control that concentrates on three-dimensional sound fields is presented.< >
Active noise control (ANC) is achieved by introducing a cancelling
“antinoise” wave through an appropriate array of secondary
sources. These secondary sources are interconnected through an
electronic system using a specific signal processing algorithm for the
particular cancellation scheme. ANC has application to a wide variety of
problems in manufacturing, industrial operations, and consumer products.
The emphasis of this paper is on the practical aspects of ANC systems in
terms of adaptive signal processing and digital signal processing (DSP)
implementation for real-world applications. In this paper, the basic
adaptive algorithm for ANC is developed and analyzed based on
single-channel broad-band feedforward control. This algorithm is then
modified for narrow-band feedforward and adaptive feedback control. In
turn, these single-channel ANC algorithms are expanded to
multiple-channel cases. Various online secondary-path modeling
techniques and special adaptive algorithms, such as lattice,
frequency-domain, subband, and recursive-least-squares, are also
introduced. Applications of these techniques to actual problems are
highlighted by several examples
The first edition of Sound and Structural Vibration was written in the early 1980s. Since then, two major developments have taken place in the field of vibroacoustics. Powerful computational methods and procedures for the numerical analysis of structural vibration, acoustical fields and acoustical interactions between fluids and structures have been developed and these are now universally employed by researchers, consultants and industrial organisations. Advances in signal processing systems and algorithms, in transducers, and in structural materials and forms of construction, have facilitated the development of practical means of applying active and adaptive control systems to structures for the purposes of reducing or modifying structural vibration and the associated sound radiation and transmission. In this greatly expanded and extensively revised edition, the authors have retained most of the analytically based material that forms the pedagogical content of the first edition, and have expanded it to present the theoretical foundations of modern numerical analysis. Application of the latter is illustrated by examples that have been chosen to complement the analytical approaches to solving fairly simple problems of sound radiation, transmission and fluid-structural coupling that are presented in the first edition. The number of examples of experimental data that relate to the theoretical content, and illustrate important features of vibroacoustic interaction, has been augmented by the inclusion of a selection from the vast amount of material published during the past twenty five years. The final chapter on the active control of sound and vibration has no precursor in the first edition. * Covers theoretical approaches to modeling and analysis * Highly applicable to challenges in industry and academia * For engineering students to use throughout their career.
Recent technological advances in the development of fast digital signal processors have made the active control of sound a practical proposition. This book brings together results from research in the two disciplinesof acoustics and signal processing and presents the fundamentals of noise control in a unified manner. Practical applications are presented wherever possible although the emphasis is on the algorithmic principles which form the foundation of practical systems. The volume is written in textbook style and aimed at both undergraduate and postgraduate students of acoustics and signal processing, professional acoustical and electrical engineers, and researchers in the field of active control.
Signal Processing for Active Control sets out the signal processing and automatic control techniques that are used in the analysis and implementation of active systems for the control of sound and vibration. After reviewing the performance limitations introduced by physical aspects of active control, Stephen Elliott presents the calculation of the optimal performance and the implementation of adaptive real time controllers for a wide variety of active control systems. Active sound and vibration control are technologically important problems with many applications. 'Active control' means controlling disturbance by superimposing a second disturbance on the original source of disturbance. Put simply, initial noise + other specially-generated noise or vibration = silence [or controlled noise]. This book presents a unified approach to techniques that are used in the analysis and implementation of different control systems. It includes practical examples at the end of each chapter to illustrate the use of various approaches. This book is intended for researchers, engineers, and students in the field of acoustics, active control, signal processing, and electrical engineering.
The low frequency sound inside a number of aircraft and cars is now attenuated using commercial active soundcontrol systems. These operate either using loudspeakers to directly drive the sound field, or with shakers acting on the structure to modify its vibration and, hence, reduce excitation of the sound field. As the structure becomes larger, the number of actuators and sensors required for effective control rises significantly. Conventional, fully coupled control systems then become costly in terms of weight and sensitivity to individual failures. An alternative strategy of distributing the control over multiple local controllers will be disucssed, which has been shown to be effective in a number of cases. The workings of the inner ear also provide a remarkable natural example of decentralised active vibration control, who's aim is to enhance the motion within the cochlea. A simple model for this cochlear amplifier will be described, in which each of the outer hair cells act as local control loops, and its use illustrated in predicting the otoacoustic emissions generated by the ear as a result of this mechanism. These emissions are used clinically to screen the hearing of young children, so it is important to understand how they are generated within the cochlea.
This paper describes a number of recent advances in the prediction of automotive interior noise. A brief review of existing modeling methods is given. Recent advances are then discussed in the following areas: (i) low frequency FE models, (ii) airborne SEA models, (iii) structure-borne SEA models and (iv) the use of CFD for source modeling.
Different polynomial chaos methods coupled to the fictitious domain approach have been applied to one- and two-dimensional elliptic problems with multi uncertain variables in order to compare the accuracy and convergence of the methodologies. Both intrusive and non-intrusive methods have been considered, with particular attention to their employment for quantification of geometric uncertainties. A Fictitious Domain approach with Least-Squares Spectral Element approximation has been employed for the analysis of differential problems with uncertain boundary domains. Its main advantage lies in the fact that only a Cartesian mesh, that represents the enclosure, needs to be generated. Excellent accuracy properties of considered methods are demonstrated by numerical experiments.
A method to find optimal locations and properties of anti-noise actuators in a local noise control system is considered. The local noise control performance is approximated by an approach based on a finite element method, attempting to estimate the average performance of an optimal active noise control (ANC) system. Local noise control uses a fixed number of circular actuators that are located on the boundary of a three-dimensional enclosed acoustic space. Actuator signals are used to minimize the known harmonic noise at specified locations. The average noise reduction is maximized at two frequency ranges by adjusting the anti-noise actuator configuration, which is a non-linear multi-objective optimization problem. To solve the optimization problem, an unsorted population size evolutionary optimization algorithm (UPS-EMOA) is considered, and its performance is compared to the widely-known NSGA-II method. As a numerical example problem, the ANC in a passenger car cabin is considered. Significantly better noise control is obtained with the optimized actuator locations than only by a engineer’s sophisticated guess.
Active control works by destructive interference between the original sound or vibration field in the vehicle and that generated by a controllable, secondary, source. Physical limitations generally confine its usefulness to low frequencies and so that it complements conventional passive control methods. The development of powerful processors at an affordable cost and the increasing trend towards integration in vehicles has allowed the commercial implementation of active control systems by several manufacturers, mainly for the reduction of low frequency engine noise. As vehicles become lighter to achieve fuel efficiency targets, it is expected that active control will play an important part in maintaining an acceptable NVH environment, in terms of sound quality as well as overall level.
RESUMEM RESUMEM
We present a mathematical framework for the active control of time-harmonic acoustic disturbances. Unlike many existing methodologies, our approach provides for the exact volumetric cancellation of unwanted noise in a given predetermined region of space while leaving unaltered those components of the total acoustic field that are deemed friendly. Our key finding is that for eliminating the unwanted component of the acoustic field in a given area, one needs to know relatively little; in particular, neither the locations nor structure nor strength of the exterior noise sources need to be known. Likewise, there is no need to know the volumetric properties of the supporting medium across which the acoustic signals propagate, except, perhaps, in the narrow area of space near the boundary (perimeter) of the domain to be shielded. The controls are built based solely on the measurements performed on the perimeter of the region to be shielded; moreover, the controls themselves (i.e., additional sources) are also concentrated only near this perimeter. Perhaps as important, the measured quantities can refer to the total acoustic field rather than only to its unwanted component, and the methodology can automatically distinguish between the two.
In the paper, we construct a general solution to the aforementioned noise control problem. The apparatus used for deriving the general solution is closely connected to the concepts of generalized potentials and boundary projections of Calderon's type. For a given total wave field, the application of Calderon's projections allows us to definitively split its incoming and outgoing components with respect to a particular domain of interest, which may have arbitrary shape. Then the controls are designed so that they suppress the incoming component for the domain to be shielded or alternatively, the outgoing component for the domain, which is complementary to the one to be shielded. To demonstrate that the new noise control technique is appropriate, we thoroughly work out a two-dimensional model example that allows full analytical consideration.
To conclude, we very briefly discuss the numerical (finite-difference) framework for active noise control that has, in fact, already been worked out, as well as some forthcoming extensions of the current work: optimization of the solution according to different criteria that would fit different practical requirements, applicability of the new technique to quasi-stationary problems, and active shielding in the case of the broad-band spectra of disturbances. In the future, the aforementioned finite-difference framework for active noise control is going to be used for analyzing complex configurations that originate from practical designs.
A tensor-based method is proposed for the solution of partial differential equations defined on uncertain parameterized domains. It provides an accurate solution which is explicit with respect to parameters defining the shape of the domain, thus allowing efficient a posteriori probabilistic or parametric analyses. In the proposed method, a fictitious domain approach is first adopted for the reformulation of the parametric problem on a fixed domain, yielding a weak formulation in a tensor product space (product of space functions and parametric functions). The paper is limited to the case of Neumann conditions on uncertain parts of the boundary. The Proper Generalized Decomposition method is then introduced for the construction of a tensor product approximation (separated representation) of the solution. It can be seen as an a priori model reduction technique which automatically captures reduced bases of space functions and parametric functions which are optimal for the representation of the solution. This tensor-based method is made computationally tractable by introducing separated representations of variational forms, resulting from separated representations of the parameterized indicator function of the uncertain domain. For this purpose, a method is proposed for the construction of a constrained tensor product approximation which preserves positivity and therefore ensures well-posedness of problems associated with approximate indicator functions. Moreover, a regularization of the geometry is introduced to speed up the convergence of these tensor product approximations.
This paper presents a review of active techniques for aerospace vibro-acoustic control. First, the mechanisms of airborne or structure-borne sound generation and transmission in aerospace vehicles are briefly reviewed. The main approaches of passive and active noise/vibration control are then summarised, and three examples of active systems that have already been developed into practical aerospace applications are briefly described. Finally the actuator, sensor, and control system requirements for aerospace applications are discussed.
This paper presents a theoretical study of the active control of both structure-borne and airborne noise transmission through a double-panel system. The physical and geometrical characteristics of the system were chosen to be similar to those of the fuselage of a civil aircraft. The total sound power transmitted by the double-panel system was used to evaluate the active control performance of four different strategies for the control system: first, active mounts connecting the two panels and loudspeakers placed between the two panels were driven to minimize the total sound power radiated by the panel (the reference case); second, active mounts connecting the two panels were driven to cancel the out-of-plane velocities at the connecting points on the radiating panel; third, loudspeakers placed between the two panels were driven to cancel the acoustic pressure at points near each control loudspeaker; and fourth, active mount and control loudspeaker systems were used simultaneously as already stated. The simulations show that the control loudspeakers are able to produce Large attenuation of the sound transmission at low frequencies close to the mass-air-mass resonance of the double panel. The performance is significantly better if the loudspeakers are driven to minimize radiated sound power, rather than cancel pressure between the panels. The active mount configuration studied in this paper does not produce significant reductions of the sound transmission except in the case where it is used in combination with the control loudspeakers.
The behavior of supersonic impinging jets is dominated by a feedback loop due to the coupling between the fluid and acoustic fields. This leads to many adverse effects when such flows occur in short takeoff and vertical landing aircraft, such as a significant increase in the noise level, very high unsteady loads on file nearby structures, and an appreciable loss in lifting during hover. In earlier studies, it was demonstrated that by using supersonic microjets one could disrupt the feedback loop that leads to substantial reductions in the aforementioned adverse effects. However, the effectiveness of control was found to be strongly dependent on the ground plane distances and the jet-operating conditions. The effect of various microjet control parameters are investigated in some detail to identify their influence on control efficiency and additional insight is provided on the physical mechanism behind this control method. Parameters studied include microjet angle, microjet pressure. and the use of microtabs instead of microjets. These results indicate that by choosing appropriate control parameters it should be possible to devise a control strategy that produces optimal control for the entire operating range of conditions of the supersonic impinging jet. Moreover, the experimental results provide convincing evidence or the generation or significant streamwise vorticity by the activation microjets. It is postulated that the generation of streamwise vorticity and its evolution in the jet How might be one of the main physical phenomena responsible for the reduction of flow unsteadiness in impinging jets.
This paper is concerned with the active control of sound fields in enclosures. Specifically, the numerical problem of determining the optimum locations of control sensors and actuators is addressed. A new method for determining the optimum secondary sources strength is proposed, based on the explicit prediction of the sound field, which makes the simulation of realistic acoustical applications feasible, in terms of the enclosure's boundary conditions. The irregular geometry of a car cabin with complex boundary conditions is used in order to demonstrate the application of the new method to a test case where the existing methods cannot theoretically apply without resolving to significant numerical error. The new method of determining the secondary sources strength is combined with a modified genetic and a gradient optimization algorithm so as to locate the optimum positions of active noise control transducers for global sound field control. The overall algorithm, constituting of the method for calculating the secondary sources' strength and the optimization algorithms, is adjusted with computational improvements for better performance.
Significant advances have been made during the past 45 years in the understanding of airplane interior noise. Noise sources and transmission paths are discussed, and methods for the prediction of interior noise are summarized. Noise control methods are reviewed, including recent work in active noise control.
The feasibility of improving the insertion loss of lightweight double panel partitions by using small loudspeakers as active noise control sources inside the air gap between both panels of the partition is investigated analytically, numerically and experimentally in this paper. A theoretical analysis of the mechanisms of the fluid-structure interaction of double panel structures is presented in order to gain insight into the physical phenomena underlying the behaviour of a coupled vibro-acoustic system controlled by active methods. The analysis, based on modal coupling theory, enables one to derive some qualitative predictions concerning the potentials and limitations of the proposed approach. The theoretical analysis is valid only for geometrically simple structures. For more complex geometries, numerical simulations are required. Therefore the potential use of active noise control inside double panel structures has been analyzed by using coupled finite element and boundary element methods. To verify the conclusions drawn from the theoretical analysis and the numerical calculation and, above all, to demonstrate the potential of the proposed approach, experiments have been conducted with a laboratory set-up. The performance of the proposed approach was evaluated in terms of relative insertion loss measurements. It is shown that a considerable improvement of the insertion loss has been achieved around the lightly damped resonances of the system for the frequency range investigated (60–220 Hz).
Experimental studies of supersonic impinging jet flows suggest that they are greatly influenced by the flow-acoustic interactions through a feedback mechanism. The self-sustained oscillations of the jet column observed in theses flows result in high velocities in the ambient medium induced by the large-scale coherent vortical structures in the jet shear layers. As a consequence, the suck down force on the surface from which the jet is issuing can reach as high as 60% of the primary jet thrust. In addition, the overall sound pressure level (OASPL), increase significantly relative to a free jet. To alleviate these undesirable flow and acoustic characteristics, a novel control technique using supersonic microjets is demonstrated. Sixteen supersonic microjets are placed around the circumference of the main jet at the nozzle exit to disrupt the feedback mechanism. As a result, significant lift loss recovery(-50%) and reduced near field OASPL (-7dB) are observed.
The current state of the art technology for predicting and controlling
noise levels inside propeller driven aircraft is reviewed. Wider aspects
of aircraft interior noise than just propeller noise are discussed
because work performed with various noise sources in mind is being
applied to propeller driven aircraft. The dominant characteristic of
propeller noise, a series of discrete frequency harmonic components,
creates a unique problem in that the cabin noise levels can depend
critically on the precise frequencies associated with the propeller
noise and the resonances of the transmitting structure and receiving
cavity. Steps to be taken before the transmission of noise into
propeller driven aircraft can be fully understood and a successful noise
control program established are listed.
A physical damping is considered as a preconditioning technique for acoustic and elastic wave scattering. The earlier preconditioners for the Helmholtz equation are generalized for elastic materials and three-dimensional domains. An algebraic multigrid method is used in approximating the inverse of damped operators. Several numerical experiments demonstrate the behavior of the method in complicated two-dimensional and three-dimensional domains.
A preconditioner defined by an algebraic multigrid cycle for a damped Helmholtz operator is proposed for the Helmholtz equation. This approach is well-suited for acoustic scattering problems in complicated computational domains and with varying material properties. The spectral properties of the preconditioned systems and the convergence of the GMRES method are studied with linear, quadratic, and cubic finite element discretizations. Numerical experiments are performed with two-dimensional problems describing acoustic scattering in a cross section of a car cabin and in a layered medium. Asymptotically the number of iterations grows linearly with respect to the frequency while for lower frequencies the growth is milder. The proposed preconditioner is particularly effective for low-frequency and mid-frequency problems.
IntroductionPrinciples of Active ControlActive Control of Free-Field SoundActive Control of Sound in DuctsActive Control of Enclosed Sound FieldsSingle-Channel Feedback Control SystemsMultichannel Feedforward Control SystemsReferences
The notion of sound is intuitively given by human perception. It is common knowledge that “audible” signals, originating at
various sources of sound and propagating through an acoustic medium, are “picked up” by the human ear. The reaction of the
eardrums to pressure changes in the air is an elementary example of vibroacoustic fluid-structure interaction. The sources
of sound can be of different nature. These notes are concerned with the computational evaluation of the sound in thin-walled
cabins like passenger compartments in cars, trains, ships, or airplanes. The walls of these cabins are in contact with an
acoustic medium that fills the interior volume of the cabin (also called the acoustic cavity). By interaction between the
fluid particles, the ocsillations at the structure-fluid interface spread through the cavity in the form of waves which are,
in general, reflected at the boundaries. The interference of incoming and reflected waves may lead to resonant standing waves.
This effect can be the cause for booming noise in vehicle cabins. It is the goal of vibroacoustic simulations to predict such
unwanted effects and to explore design variants that are aimed at reducing the noise level over the frequency range of interest.
Speaking more generally, the goal of the simulations consists in a realistic computational evaluation of the vibroacoustic
comfort level. A basic knowledge of the underlying physical effects and their mathematical formulation is essential for the
setup of suitable computational models as well as for the interpretation of the numerical results.
The principles of acoustic and vibroacoustic reciprocity are explained. Examples are then given of applications of acoustic
reciprocity to the experimental analysis of sound radiation by various systems of interest to noise control engineers. The
final part of the paper is devoted to a presentation of examples of the practical application of Lyamshev reciprocity to problems
of identifying and quantifying sources of noise that operate in a variety of engineering systems.
The main purpose of this work is the implementation and experimental investigation of different active structural acoustic control (ASAC) concepts for the reduction of interior noise in an automobile passen-ger compartment. For the control experiments, a medium-class test car was used, which had been equipped with an active windshield. The active windshield consists of the serialproduction laminated glass pane augmented with piezoceramic patch-transducers applied to theblackened rim of the wind-shield. A multi-reference test provided measurement data for the identification of a local discrete-time state-space model (SSM). The subsequent acquisition of frequency response functions (FRF) by way of using the same actuators but measuring on a much finer grid provided the database for the formulation of a least-squares problem to derive a global system model. Based on the local and global discrete-time SSMs, different controllers were designed and experimentally realized. The comparison of the vibration levels in open- and closed-loop showed a global reduction of 5 dB to 7 dB in the acoustically relevant frequency band containing the second and third structural resonance of the windshield system. The occurrence of complex operational deflection shapes (ODS) was identified as the main limitation con-cerning the disturbance rejection of the active system. The acoustic performance of the ASAC system is reflected in a reduction up to 15 dB in sound pressure level (SPL).
The design of active noise control (ANC) has been developed in the last two decades based on linear identification and control tools. However, acoustic processes present nonlinearities coming both from the characteristics of the actuator and from the nature of the process. Recent research has emphasized the importance of nonlinear model-based controllers, which increase the performance of several types of systems. From the different nonlinear techniques, fuzzy modeling is one of the most utilized. Direct and inverse multivariable fuzzy models can be identified directly from data using fuzzy clustering. Inverse models can then be applied directly as controllers, which can be included in an active noise control scheme. This paper proposes the use of fuzzy techniques in ANC. The performance of the proposed control schemes is compared to classical finite impulse response ANC in an experimental setup. The proposed fuzzy control scheme outperforms classical active noise controllers.
A general method is presented to optimize transducer location in an active noise control problem. The method includes two parts. First, the actuator configuration is determined by using a model of the primary field which is a spherical harmonics expansion. In the second part, a genetic algorithm is used to determine the error sensor configuration. This method is then applied to two real acoustic sources: a dipole and an electrical transformer. In numerical simulations, the primary field of both sources measured in an anechoic room was used to determine the active control configurations. Then, the actuator and error sensor arrangement was tested in an active control experiment involving both primary, sources.
This numerical simulation uses multiple linear regression with subset selection to optimize the locations of control actuators in a feedforward active noise control system. By formulating the feedforward control problem as a regression, subset selection can find the actuator locations that provide the best system performance. Subset selection provides benefits over continuous optimization approaches because of its computational efficiency; subset selection can examine systems for which the system response is expensive to compute, such as fluid–structure interaction problems, and can efficiently optimize large numbers of actuators. This paper describes a method for exhaustive-search subset selection, and provides numerical results for a simple active structural-acoustic control problem.
For vehicle under normal driving conditions and speeds above 30–40 km/h the dominating internal and external noise source is the sound generated by the interaction between the tyre and the road. This paper presents a simple model to predict tyre behaviour in the frequency range up to 400 Hz, where the dominant vibration is two dimensional. The tyre is modelled as an elemental system, which permits the analysis of the low-frequency tyre response when excited by distributed stochastic displacements in the contact patch. A linear model has been used to calculate the contact forces from the road roughness and thus calculate the average spectral properties of the resulting radial velocity of the tyre in one step from the spectral properties of the road roughness. Such a model has also been used to provide an estimate of the potential effect of various active control strategies for reducing the tyre vibrations.
Numerical simulation has been used to predict the reduction of acoustic potential energy in a mobile mining vehicle cabin as a result of active noise control (ANC). Resonance frequencies and mode shapes of both the structural and cavity modes were calculated using a finite element (FE) model. Modal coupling analysis was used to determine the coupled response of the model to an interior acoustic source, and the results were compared to measurements taken inside the cabin. Correlation between the FE model and physical measurements was improved to the extent that the model could be used to predict the effect of ANC in the cabin for different configurations of control sources and error sensors. As expected from previous work, it was found that the acoustic potential energy inside the cabin could be significantly reduced if a control source is placed in close proximity to the primary volume velocity source. However, increasing the number of sensors and/or increasing the number of control sources located remotely from the primary source had little impact on the achievable reduction in the overall acoustic potential energy in the cabin. This supported results obtained in off-line experiments using control source to error sensor transfer function measurements and quadratic optimization theory, where it was found that good reduction at the error sensors was possible inside the mining vehicle cabin but that global control was not feasible using sources remotely located from the primary source.
Active control solutions appear to be a feasible approach to cope with the steadily increasing requirements for noise reduction in the transportation industry. Active controllers tend to be designed with a target on the sound pressure level reduction. However, the perceived control efficiency for the occupants can be more accurately assessed if psychoacoustic metrics can be taken into account. Therefore, this paper aims to evaluate, numerically and experimentally, the effect of a feedback controller on the sound quality of a vehicle mockup excited with engine noise. The proposed simulation scheme is described and experimentally validated. The engine excitation is provided by a sound quality equivalent engine simulator, running on a real-time platform that delivers harmonic excitation in function of the driving condition. The controller performance is evaluated in terms of specific loudness and roughness. It is shown that the use of a quite simple control strategy, such as a velocity feedback, can result in satisfactory loudness reduction with slightly spread roughness, improving the overall perception of the engine sound.
We consider a problem of eliminating the unwanted time-harmonic noise on a predetermined region of interest. The desired objective is achieved by active means, i.e., by introducing additional sources of sound called control sources, that generate the appropriate annihilating acoustic signal (anti-sound). A general solution for the control sources has been obtained previously in both continuous and discrete formulation of the problem. In the current paper, we focus on optimizing the overall absolute acoustic source strength of the control sources. Mathematically, this amounts to the minimization of multi-variable complex-valued functions in the sense of L1 with conical constraints, which are only "marginally" convex. The corresponding numerical optimization problem appears very challenging even for the most sophisticated state-of-the-art methodologies, and even when the dimension of the grid is small, and the waves are long. Our central result is that the global L1-optimal solution can, in fact, be obtained without solving the numerical optimization problem. This solution is given by a special layer of monopole sources on the perimeter of the protected region. We provide a rigorous proof of the global L1 minimality for both continuous and discrete optimization problems in the one-dimensional case. We also provide numerical evidence that corroborates our result in the two-dimensional case, when the protected domain is a cylinder. Even though we cannot fully justify it, we believe that the same result holds in the general case, i.e., for multi-dimensional settings and domains of arbitrary shape. We formulate it as a conjecture at the end of the paper.
Recently, a new strategy was proposed to solve stochastic partial differential equations on random domains. It is based on the extension to the stochastic framework of the eXtended Finite Element Method (X-FEM). This method leads by a ``direct'' calculus to an explicit solution in terms of the variables describing the randomness on the geometry. It relies on two major points: the implicit representation of complex geometries using random level-set functions and the use of a Galerkin approximation at both stochastic and deterministic levels. In this article, we detail the basis of this technique, from theoretical and technical points of view. Several numerical examples illustrate the efficiency of this method and compare it to other approaches.
Active control of sound results from destructive interference
between the sound field of an original acoustic source and that from a
controllable array of `secondary' acoustic sources. For this destructive
interference to occur over an appreciable region of space the sound
field of the secondary sources must match that from the primary source
in both time and space. The spatial matching requirement leads to an
upper frequency of applicability of active control. Active control
complements conventional passive methods of sound control, which do not
work well at low frequencies. Practical feedforward controllers, using a
multichannel generalisation of the well known LMS adaptive algorithm,
have been developed, using as many as 16 loudspeakers and 32
microphones, and applied with considerable success in the control of
low-frequency propeller noise inside aircraft and low-frequency engine
noise inside cars. The authors describe such systems
An active control system for low-frequency road noise in
automobiles combined with an audio system is developed as a commercial
application for the first time in the world, and installed in a station
wagon. The purpose of this paper is to provide an outline of the system
and describe the newly developed cost-reduction technology used for it,
since the reduction of system costs is a major reason that active noise
control technology could successfully be applied in a commercial
product. The methods used to reduce costs include utilization of
feedback control, implementation by analogue circuits, and common use of
audio system speakers. This system reduces low-frequency road noise in
the front seat by about 10 dB and improves audio system listening
experience while driving
A consistent framework is presented for the calculation of the
optimal performance of feedforward and feedback control systems in
attenuating random disturbances. In both cases, the optimization problem
is transformed into a quadratic form using an internal model of one part
of the physical system under control. The resulting architecture for the
feedback controller is known as internal model control (IMC) and is
widely used in the H<sub>∞</sub> control literature. With this
controller architecture, the optimum performance of a multichannel
feedback system can be readily calculated using the quadratic
optimization techniques already developed in the sampled time domain for
multichannel feedforward control. The robustness of the stability of
such a feedback controller to changes in the plant response can be
separately assessed using a generalization of the complementary
sensitivity function, which has a particularly simple form when IMC is
used. The stability robustness can be improved by incorporating various
forms of effort weighting into the cost function being minimized, some
of which are already used for adaptive feedforward controllers. By way
of example, the performance is calculated of both feedforward and
feedback controllers for the active attenuation of road noise in cars.
The variation of performance with loop delay is calculated for both
types of control, and it is found that in this example, the potential
attenuation is greatest using feedback control but only if the loop
delay is less than 1.5 ms
A novel method of performing acoustic echo cancelling using
microphone arrays is presented. The method employs a digital
self-calibrating microphone system. The calibration process is a simple
indirect on-site calibration that adapts to the particulars of the
acoustic environment and the electronic equipment in use. Primarily
intended for handsfree telephones in automobiles, the method
simultaneously suppresses the handsfree loudspeaker and car noise. The
system also continuously takes into account disturbances such as fan
noise. Examples from an extensive evaluation in a car are also included.
Typical performance results demonstrate 20-dB echo cancellation and
10-dB noise reduction simultaneously
- S Elliott
- P Nelson
S. Elliott, P. Nelson, Active noise control, Vol. 10, IEEE, 1993.