Warmstarting the Constrained Optimal Filter Design Problem for Active Noise Control Systems in Conic Formulation

In practical active noise control (ANC) systems, constraints such as stability, need to be considered in the controller design process. The optimal control filters can be obtained by solving a constrained optimization problem, which requires a significant computational effort. Recently, a convex formulation in conic form was proposed for ANC applications which was shown to result in a computational time reduction by several orders. It is desirable to further improve its efficiency so that the optimal filter design process can be continuously repeated to achieve adaptive control for slow varying operating conditions. One potential way is to introduce a warmstart technique where the filter solution of a similar system or environment is used as the starting point of the optimization algorithm. However, the conic formulation should be solved by the interior-point method which, in general, is challenging for applying warm start techniques. In the current work, modifications are proposed to the original ANC filter design formulation so that the warmstart techniques can be applicable. The performance of warmstarting technique is investigated. Results show that an appropriate choice of warmstart strategy can significantly reduce the number of iterations required for solving the proposed conic formulation of ANC filter design problem

A Review of Theories for Sound Transmission through Infinite Double Panels and Identification of Asymptotic Behavior

In this paper, existing theories for sound transmission through infinite, double panel systems are first reviewed with a view to identifying their differences. The review begins from the classic papers of Beranek and Work, and London, before going on to consider later work by Mulholland, Parbrook and Cummings, Heckl, Fahy, and Hamada and Tachibana. The sound transmission problem was framed as a boundary value problem by most of these authors, except for Mulholland et al. who derived a multiple-reflection theory, and Hamada and Tachibana who introduced a transfer matrix approach. Further, except for Heckl’s model, in which a locally-reacting medium is assumed to exist between the panels, the main difference between the models lies in the form of the panel impedance adopted by the various authors, with some authors considering only limp panels, while others allowed for the panels’ flexural stiffness. Finally, an analysis of the high frequency asymptotic behavior of flexurally-stiff, double panels above their critical frequencies is presented. In that analysis, it was found, for example, that the peaks in the transmission loss increase at a rate of 120 dB/dec, while the minima increase at rate of 60 dB/dec

A Transfer-Matrix-Based Approach to Predicting Acoustic Properties of a Layered System in a General, Efficient, and Stable Way

Layered materials are one of the most commonly used acoustical treatments in the automotive industry, and have gained increased attention, especially owing to the popularity of electric vehicles. Here, a method to model and couple layered systems with various layer types (i.e., poro-elastic layers, solid-elastic layers, stiff panels, and fluid layers) is derived that makes it possible to stably predict their acoustical properties. In contrast with most existing methods, in which an equation system is constructed for the whole structure, the present method involves only the topmost layer and its boundary conditions at two interfaces at a time, which are further simplified into an equivalent interface. As a result, for a multi-layered system, the proposed method splits a complicated system into several smaller systems and so becomes computationally less expensive. Moreover, traditional modeling methods can lose stability when there is a large disparity between the magnitudes of the waves within the layers (e.g., at higher frequencies, for a thick layer, or for extreme parameter values). In those situations, the contribution of the most attenuated wave can be masked by numerical errors, hence inducing instability when inverting the system. Here, the accuracy of the wave attenuation terms is ensured by decomposing each layer’s transfer matrix analytically and reformulating the equation system. Therefore, this method can produce a stable prediction of acoustical properties over a large frequency and parameter region. The fact that the proposed method can couple different layer types in a general, efficient, convenient, and stable way is beneficial, for example, when numerically optimizing the design of the acoustical treatments. The predicted acoustic properties of layered systems calculated using the proposed method have been validated by comparison with those predicted by previously existing methods. Further, an optimal design exercise is performed to find a lightweight layered dash panel treatment

Experimental Study and Modeling of the Level-Dependent Acoustical Behavior of Granular Particle Stacks

Researchers have previously observed elastic modulus softening and increased damping when granular particle stacks are exposed to progressively increasing acoustical excitation levels. However, the level-dependent behavior of granular particle stacks is not well understood, and there are no comprehensive approaches to modeling those effects. Earlier, the authors measured the absorption coefficient of a stack of one type of granular activated carbon stack by using signals having different bandwidths and levels. In the present work, five more types of granular particle stacks were studied to validate and generalize the previous conclusions: i.e., both the modulus softening, and increased damping can be characterized by the total RMS fluid displacement at the sample surface. Therefore, a strain-dependent modulus and damping formula from the literature (based on cyclic loading tests on sand particles) was converted into a total RMS fluid displacement-dependent formula (based on acoustic measurements). In addition, a multi-layered model based on this displacement-dependent formula has been developed to iteratively update each layer’s modulus, damping, and total RMS fluid displacement to solve for the particle stack’s acoustic properties. This approach allows modeling of the particle stack’s acoustical behavior by using a single set of parameters, even for different level and bandwidth test signals

A General Stable Approach to Modeling and Coupling Multilayered Systems with Various Types of Layers

In this article, a general method is proposed to model layered systems with two-by-two transfer matrices, and further, to solve for the acoustic absorption, reflection, and transmission coefficients. Since the proposed method uses the matrix representation of various layers and interfaces from the Transfer Matrix Method (TMM), the equation system can be established efficiently. However, the traditional TMM can lose stability when there is a large disparity between the magnitudes of the waves traveling in opposite directions within the layers (i.e., at higher frequencies, for a thick layer, or for extreme parameter values). In such cases, the contribution of the most attenuated wave can be masked by numerical errors and can induce instability when solving the system. Therefore, in the proposed method, to stabilize the calculated acoustic properties of the system, the principle is to ensure the accuracy of the wave attenuation terms by decomposing each layer’s transfer matrix and reformulating the equation system. This method can couple different layer types in a general way and is easy to assemble and implement with numerical code. The predicted acoustic properties of layered systems calculated using the proposed method have been validated by comparison with those predicted by other existing methods

Four-Microphone Measurement of Transmission Loss of Automotive Door Seals: Improved Correction Factor

Recently, a desktop procedure for measuring the transmission loss of automotive door seals was proposed. In that procedure, a door seal is placed in a square-section, four-microphone standing wave tube, and is held between a movable clamp and the opposite tube wall. Since the clamp partially blocks the tube cross-section, it is necessary to correct the measured transmission loss to obtain the transmission loss of the seal alone. Initially, the correction factor was determined by measuring transmission losses of samples having known properties, and that were clamped in the tube in the same way as the seals. It would be desirable if those samples had transmission losses comparable to the seals, but the original materials had transmission losses much lower than the seals. Since it was not possible to find materials having the desired, high transmission loss, the correction factor has now been determined by using a finite element model of the measurement arrangement, in which the “sample” was represented as a porous material whose properties were adjusted to yield transmission losses similar to the door seals. The procedure by which the new correction factor was determined will be described in detail and a general expression for the correction factor will be given

Impacts of road network expansion on landscape ecological risk in a megacity, China: A case study of Beijing

AbstractRoad networks affect the spatial structure of urban landscapes, and with continuous expansion, it will also exert more widespread influences on the regional ecological environment. With the support of geographic information system (GIS) technology, based on the application of various spatial analysis methods, this study analyzed the spatiotemporal changes of road networks and landscape ecological risk in the research area of Beijing to explore the impacts of road network expansion on ecological risk in the urban landscape. The results showed the following: 1) In the dynamic processes of change in the overall landscape pattern, the changing differences in landscape indices of various landscape types were obvious and were primarily related to land-use type. 2) For the changes in a time series, the expansion of the road kernel area was consistent with the extension of the sub-low-risk area in the urban center, but some differences were observed during different stages of development. 3) For the spatial position, the expanding changes in the road kernel area were consistent with the grade changes of the urban central ecological risk, primarily because both had a certain spatial correlation with the expressways. 4) The influence of road network expansion on the ecological risk in the study area had obvious spatial differences, which may be closely associated with the distribution of ecosystem types

Modeling of a Flexible Perforated Membrane Backed by Granular Materials

It has recently been shown that adding activated carbon particles to the interior of a Helmholtz resonator can improve the resonator’s absorption at low frequencies. A similar improvement has been found when a layer of activated carbon partially fills the space behind a finite, tensioned impermeable membrane. In that case, absorption peaks due to the modal response of the tensioned membrane were found to be significantly enhanced in the low frequency range. In the present work, the modeling aspects of the latter work are extended in a number of ways. First, the circular membrane is considered to be both tensioned and flexurally stiff, and further, it is micro-perforated: i.e., it has a finite flow resistance. Secondly, the particle layer behind the membrane is modeled by using a finite difference procedure that accounts for interaction of the particle layer and walls that contain it: i.e., the particle stack itself is allowed to exhibit modal behavior in the radial direction. Finally, the interaction of the membrane nearfield and the particle stack is fully accounted for. It is shown that previously observed behavior can be reproduced, and further that the modal behavior of the particle stack may also enhance the system’s absorption

Study of the Impact of Boundary Conditions on Acoustical Behavior of Granular Materials and their Implementation in the Finite Difference Method

Granular materials display significant differences in their acoustical response when tested in a standing wave tube, compared with the behavior of more traditional sound absorbing materials such as fibrous webs and foams. The latter materials can often be modeled as an equivalent fluid with the further assumption that the material properties do not depend on the input signal level. In contrast, the level dependence of the acoustical behavior of granular materials has been observed in measurements of glass bubbles, as reported in previous studies, for example. When the input level is low, the absorption coefficient of the glass bubble stack shows solid-like behavior with multiple peaks associated with modal response of the stack. On the other hand, when the input level is high, glass bubble stacks show fluid-like behavior, with the quarter wavelength resonance in the direction of the tube axis dominating the response. In the current work, the boundary conditions at the air/granule interface and the granule/tube wall boundary are studied, as is the mechanism causing the variation of the apparent stiffness of the granule stack. The proposed model is implemented with a finite difference approach, and the model predictions are compared with acoustic measurements of granule stacks

Experimental Study of Granular Activated Carbon Stacks’ Level- and Time-Dependent Behavior

Granular materials, such as activated carbon, have shown advantages in absorbing low-frequency sounds, but they also exhibit significant nonlinearities. In this article, three unique types of granular particle stacks\u27 acoustical behavior are described and experimentally analyzed. First, when measuring the sound absorption spectra of particle stacks with varying depths and sample holder sizes, it was found that the frictional interaction with the tube circumferential wall can significantly affect the measurements, and a 1-D plane-wave model is only valid when the sample is thin. Secondly, when granular samples were tested with increasing excitation levels, the results indicated a decreased modulus and an increased damping. By further varying excitation level and bandwidth, a displacement- related metric was identified to describe this behavior. Thirdly, when measuring particle stacks over a longer period, the stack\u27s resonance peak gradually shifts to a higher frequency as the sample consolidates. This shift in frequency was proportional to log(Time)