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Abstract

The active casing approach is a technique to reduce noise emission of devices and machinery by controlling vibrations of their casings. This method was successfully validated by the authors for a single-panel casing in previous publications. However, if even higher noise reduction is required, a dedicated double-panel structure can be employed. In this paper, the sound insulation efficiency of a double-panel active casing is evaluated and compared with a single-panel structure by performing a series of laboratory experiments. The least mean squares algorithm is used to adaptively update control filter parameters. A low-frequency noise in the range up to 500 Hz is considered. Advantages and limits of the proposed approach are pointed out and discussed, and conclusions for future research are given.

Keywords

Active casing double panel active noise control active vibration control active structural acoustic control adaptive control

Introduction

An excessive noise generated by devices and machinery constitutes a subject of high interest to customers, producers and scientists. In a working environment, prolonged exposure to high-level noise can lead to hearing damage. Noise often causes exasperation and difficulties in communication between staff, thereby increasing a risk of an accident. In turn, household appliances can also be a source of noise, although they are not characterized by the sound pressure level, which can lead to health damage. However, it causes annoyance and significantly obstructs work or leisure, and hence the level of generated noise is gaining significance as a criterion in product selection by the consumers.

A classical protection solution is to apply passive methods of noise reduction—sound insulating materials, vibrational isolators, personal protection means, etc. However, these methods are usually ineffective for low frequencies. Moreover, they are often infeasible or inapplicable due to increase in size and weight of the device and heat exchange inefficiency. Personal protection means (earplugs, earmuffs, etc.) in turn, often limit the ability to work effectively and are inconvenient to device users or workers.

Alternatively, active control methods can be applied, which are not limited by such restrictions.^1–4 In particular, active structural acoustic control (ASAC) has been extensively used to reduce noise passing through individual barriers.⁵ Different control strategies have been examined over the years.^6,7 The sound radiation of a clamped plate has been analyzed.⁸ Double panels have also been investigated in the literature.^9,10 Usually, double-glazed windows were considered,¹¹ but also control of aircraft fuselage or building walls were concerned. One of the significant issues for double-panel structures, which should be taken into account is the mass-air-mass resonance. In proximity of the resonance frequency such structure features acoustic transmission loss even lower than that for equivalent single panel.¹² Moreover, it is shown in the literature that symmetric double-panel structures may result in lack of observability, if the active control system is based on measurements by microphones located in the cavity between the panels.¹³ However, this issue can successfully be mitigated if asymmetric structures are implemented.

The aim of this paper is to extend the aforementioned studies by controlling vibration of whole casings of devices generating excessive noise. The idea of single-panel active casings has already been explored by the authors and has proven its effectiveness. The method considered in this paper consists in control of multiple double-panel casing walls by applying sensors and actuators in different configurations (three cases are evaluated). The method results in reduction of noise emission to the surrounding environment when appropriately implemented. Therefore, it allows for achieving global reduction instead of local zones of quiet.

The paper is organized as follows. Firstly, in the upcoming section an ASAC system using a feedforward adaptive control strategy with the Normalised Leaky FxLMS algorithm is presented. Then, the laboratory setup used to examine the single- and double-panel casings is described, along with an analysis of vibrational and acoustic paths. Subsequently, experimental results for different sensors and actuators configurations are presented. Finally, the advantages and limits of the proposed approach are pointed out and discussed, and conclusions for future research are drawn.

This paper is an extended version of the paper¹⁴ published as conference materials of the 12th Conference on Active Noise and Vibration Control Methods, in response to an invitation of the Conference Organizers, and it brings new results and new analysis.

Adaptive feedforward control system

A multichannel feedforward control system is presented in this section, which is used in laboratory experiments described in the following sections.¹⁴ It is based on the Leaky Normalized Filtered-x Least Mean Square algorithm, which is used to adaptively update control filter parameters. The adaptivity is employed to respond to possible nonstationarity of the primary disturbance and changes of the plant.

The control algorithm is schematically presented in Figure 1.¹⁴ Symbol X is the reference path, W is the adaptive control filters matrix (of dimension (I × 1), where I is the number of actuators), P is the primary paths vector (of dimension (J × 1), where J is the number of error sensors), defined between the reference and error sensors. Figure S stands for the secondary paths matrix of dimension (J × I) defined between the inputs of the actuators and outputs of the error sensors. These paths include electronics necessary for signal conditioning and data conversion. The symbol Ŝ stands for the secondary path model.

Figure 1.

Multichannel feedforward control system with the FxLMS algorithm.

In turn, x(n) is the scalar reference signal, r(n) is the filtered-reference signals matrix of dimension (J × I), u(n) is the control signals vector of dimension (I × 1). Further, signals d(n) and e(n) are the primary disturbances vector and the error signals vector, respectively, both of dimension (J × 1), at positions of the error sensors where noise reduction is desired. In the control system for each casing wall, number of actuators I = 3. On the other hand, depending if microphone or accelerometers are used, number of error sensors J = 1 or J = 3, respectively. Actuators and sensors are further described in the following section.

The coefficients of ith control filter at the (n + 1)-st sample, w_i(n + 1), are updated for each of the error signals e_j(n) according to the formula $w_{i} (n + 1) = α w_{i} (n) - μ (n) r_{i j} (n) e_{j} (n)$ (1)where $w_{i} (n) = {[w_{i, 0} (n), w_{i, 1} (n), …, w_{i, N - 1} (n)]}^{T}$ is the vector of coefficients of the ith adaptive finite impulse response (FIR) control filter at sample n, and N is the filter order. Symbol $r_{i j} (n) = {[r_{i j} (n), r_{i j} (n - 1), …, r_{i j} (n - (N - 1))]}^{T}$ is a vector of regressors of the ijth filtered-reference signal, μ(n) is a step-size, and $0 < < α < 1$ is the leakage coefficient.

The ith control filter is used to calculate ith control signal, u_i(n), obtained as follows $u_{i} (n + 1) = w_{i} {(n)}^{T} x_{u} (n)$ (2)where $x_{u} (n) = {[x (n), x (n - 1), …, x (n - (N - 1))]}^{T}$ is the vector of regressors of the reference signal. The ij-th filtered-reference signal is calculated as $r_{i j} (n) = {\hat{s}}_{i j} {(n)}^{T} x_{r} (n)$ (3)where ${\hat{s}}_{i j} (n) = {[{\hat{s}}_{i j, 0} (n), {\hat{s}}_{i j, 1} (n), …, {\hat{s}}_{i j, M - 1} (n)]}^{T}$ is the vector of coefficients of the Mth order FIR model of the ijth secondary path. The models have been identified at the beginning of the experiment using a random excitation signal. In turn, $x_{r} (n) = {[x (n), x (n - 1), …, x (n - (M - 1))]}^{T}$ is a vector of regressors of the reference signal. For multichannel versions it is justified to consider the reduction of the computational burden, as discussed in Dariusz et al.¹⁵

The active casing

The active casing constructed by the authors is presented in Figure 2. It consists of a rigid and heavy cubic frame made of 3 mm thick welded steel profiles. The high rigidity of the frame assures that its resonance frequencies are far above the dominating frequencies of the noise considered. The side walls of the casing enable mounting of single or double panels. The top wall is made of a single panel in all experiments. Each plate is clamped to the structure by additional square frame and 20 screws embedded in the cubic frame. Hence, fully clamped boundary conditions are assumed for the panels. If double panels are mounted, the distance between them is 50 mm. The plate closer to the casing interior is called the incident plate, and the outer plate is referred to as the radiating plate.¹² To avoid unobservable resonances in the cavity between the double panels,¹³ the incident and radiating plates are of different thicknesses (1 mm and 2 mm, respectively). The top wall is made of 2 mm thick plate. All plates used in the experiments reported in this paper are made of aluminum. Dimensions of the structure are shown in Figure 3(a).¹⁴

Figure 2.

A photograph of the cubic active casing made of a rigid frame with aluminum walls. Only incident plates are mounted. Cavity microphones are also visible.

Figure 3.

Schematic representation of the laboratory setup and actuators and sensors arrangement: (a) schematic representation of the laboratory setup. All dimensions are given in mm; (b) locations of actuators (on the left) and sensors (on the right).

To control vibrations of the casing walls, inertial exciters NXT EX-1 are used. They are light-weight (115 g) actuators of small dimensions (70 mm), compared to the size of the casing. They are mounted on the incident plates from the inner side. Three actuators per panel are used. Their placement is a result of the optimization process using a method that maximizes a measure of the controllability of the system. The impact of the mass of the actuators is taken into account in the optimization procedure. As sensors for control purposes, microphones (Beyerdynamic MM-1) or accelerometers (Analog Devices ADXL203) are used, depending on the chosen control configuration. In case of single panels, the accelerometers are collocated with the actuators. For double panels, they are mounted on the radiating plate at locations calculated according to the method that maximizes a measure of the observability of the system.¹⁶ The placement of actuators and sensors is identical for each wall. Locations of both sensors and actuators are shown in Figure 3(b).

The laboratory room length and width is equal to 5.8 m and 3.5 m, respectively. Walls are covered with sound-absorbing materials; however, due to equipment and other object in the room, it represents acoustic properties of a common real environment, rather than an acoustic chamber.

The feedforward control system is implemented and evaluated in this research, therefore the reference signal is obtained by a microphone placed next to the loudspeaker inside the casing enclosure (referred to further as the reference microphone). In front of each casing wall, a microphone is placed in the distance of 500 mm (referred to as the outer microphone). If double panels are used, a microphone is also placed in the cavity between them (referred to as the cavity microphone, visible in Figure 2). These microphones are used for control-related purposes. Additionally, to evaluate the noise reduction efficiency, three microphones are placed at several larger distances from the casing, corresponding to potential locations of the device user (referred to as the room microphones).

The casing is placed on a basis, which is vibrationally and acoustically insulated. In the performed experiments, a loudspeaker placed on this basis is used as the primary noise source. It allows for creating an environment more suitable for the research than a real operating device, which will be used in due course.

The FIR models of secondary paths have been identified using a random excitation signal. It follows from the analysis (a set of exemplary amplitude and phase responses of secondary paths is shown in Figures 4 and 5) that the direct paths between actuators and accelerometers mounted on the same wall are of similar magnitude in the whole frequency range considered (see Figure 4(a)). In turn, the magnitudes of cross paths between actuators mounted on one wall and accelerometers mounted on the other wall are many times weaker, compared to magnitudes of direct paths within the same wall (see Figure 4(b)). This is due to the heavy and rigid frame of the casing, isolating vibrationally individual walls. Hence, the interference with each other is mainly through the acoustic field. Therefore, since such separation has been noticed, each wall is controlled individually in this research in order to simplify the algorithm and reduce computational complexity.

Figure 4.

Exemplary amplitude responses of secondary paths: (a) direct paths between actuators no. 0–2 and the accelerometer no. 0 mounted on the front wall; (b) cross paths between actuators no. 0 mounted on different walls and the accelerometer no. 0 mounted on the front wall; (c) direct paths between actuators no. 0–2 and the outer microphone assigned to the front wall; (d) cross paths between actuators no. 0 mounted on different walls and the outer microphone assigned to the front wall.

Figure 5.

Exemplary phase responses of secondary paths: (a) direct paths between actuators no. 0–2 and the accelerometer no. 0 mounted on the front wall; (b) cross paths between actuators no. 0 mounted on different walls and the accelerometer no. 0 mounted on the front wall; (c) direct paths between actuators no. 0–2 and the outer microphone assigned to the front wall; (d) cross paths between actuators no. 0 mounted on different walls and the outer microphone assigned to the front wall.

Analogous behavior can be observed for the paths between actuators and outer microphones, but only for low frequencies up to 250 Hz. Above this frequency, the cross paths between actuators mounted on one wall and an outer microphone placed in front of another wall become of similar magnitude as the direct paths between actuators and an outer microphone assigned for the same wall (see Figures 4(c) and (d)). Such couplings affect the performance of active noise control systems and it is noticed in experimental results presented in the following section.

Experimental results

In the performed experiments, all walls of the casing, except the basis, are controlled to reduce the emission of noise generated by a primary disturbance source enclosed in the casing. The primary noise signal is generated as a tonal signal of frequency incremented by 1 Hz in the range from 20 to 500 Hz. To achieve the goal of noise reduction, instantaneous square values of error signals are minimized by feedforward adaptive control systems, controlling together 15 inertial actuators (three per wall). Each of casing walls is controlled separately to reduce the computational complexity of the control algorithm. Depending on the particular configuration, the error signals are obtained by the outer microphones, the cavity microphones or by accelerometers. The control performance is evaluated as noise reduction level observed by the room microphones. Although this paper is focused on the double-panel configuration, performance of the single-panel structure is also evaluated for a comparison.

For each frequency of the primary disturbance, a 15 s experiment was performed. In its initial 4 s the active control was off, and variance of the signal acquired by different sensors was estimated as the reference point. Then, the active control was turned on. When the adaptive control algorithm converged, final 4 s of the experiment was used to estimate the variance of the signal acquired by corresponding sensors.

Results of an exemplary experiment for the frequency of the primary disturbance equal 96 Hz are shown in the time domain in Figure 6. Initial three rows present control signals, where the convergence rate can be observed. In the fourth row, signals measured by microphones used in this experiment as error sensors are presented. In the fifth row of the figure, signals measured by three room microphones are given. The reference microphone measurement is also shown for completeness.

Figure 6.

Time plots for the experiment performed for primary disturbance of 96 Hz and double-panel casing. Microphones placed in cavities of the side walls and the outer top microphone were used as error sensors.

In Figures 7 to 9, frequency characteristics for experiments with different error sensors configurations are presented. In the last rows of these figures, the mean reduction obtained at the room microphones is shown. It is considered as the main point for evaluation of active control performance. Remaining plots present variances in dB scale of signals acquired by error sensors and individual room microphones, without (red) and with (green) control.

Figure 7.

Frequency characteristics for the experiment performed for double-panel casing. Microphones placed in cavities of the side walls and the outer top microphone were used as error sensors.

Figure 8.

Frequency characteristics for the experiment performed for double-panel casing. The outer microphones were used as error sensors.

Figure 9.

Frequency characteristics for the experiment performed for double-panel casing. Accelerometers were used as error sensors.

Finally, a comparison of mean reduction levels obtained for the double-panel casing with different error sensors configurations is presented in Figure 10. In Figure 11, corresponding reduction levels for single-panel structure are presented.

Figure 10.

Comparison of mean reduction measured by room microphones. Frequency characteristics for experiments performed for double-panel casing.

Figure 11.

Comparison of mean reduction measured by room microphones. Frequency characteristics for experiments performed for single-panel casing.

Conclusion

In the performed active control experiments both single- and double-panel structures have been evaluated. The feedforward adaptive control system with the Normalised Leaky FxLMS algorithm has been used. Each wall has been controlled separately in order to simplify the algorithm and reduce computational complexity. System performance has been evaluated for different error sensors configurations. Significant levels of global noise reduction have been achieved, confirming high potential of the active casing approach to reduce excessive device noise.

The employment of outer microphones to obtain error signals offered better performance for single-panel structure than in case of double panels. This is the result of actuators mounting on the incident panels. Nevertheless, the double-panel structure introduced higher passive attenuation than single panels, and therefore the noise was more reduced in total. Moreover, the strategy of independent control system for each wall performed well for low frequencies up to 250 Hz, where as shown in the “Active casing” section, an impact of vibrations of one wall due to actuators mounted on another wall is significantly weaker, than the impact of actuators mounted directly on the wall. However, above this frequency the cross paths between different walls become significant. Thus, the independent control provides weaker performance than for lower frequencies (even the entire system may become unstable due to the couplings). This issue can be mitigated by using more sophisticated strategies, e.g. the Switched-error FxLMS algorithm, what is considered in other publications. However, it is noteworthy that these strategies require more computational power.

For double-panel casing, the configuration employing cavity microphones as error sensors performed better, than with outer microphones. The control performance was more stable and convergence problems or noise enhancement never occurred until the frequency of 400 Hz (analogous independent control strategy was employed). Moreover, such configuration is more feasible for practical implementation. Usually, users cannot agree to keep error microphones around the casing. Additionally, cavity microphones can operate with lesser gain, than outer microphones. Hence, they are less vulnerable to external disturbances. Therefore, for double-panel structures cavity microphones are more recommended as error sensors than the outer microphones. Additionally, the Switched-error FxLMS algorithm can also be employed with cavity microphones to extend further the operating frequency range.

The performance of configurations using accelerometers to obtain error signals was generally inferior to those using microphones (if the signals are used directly, without any modification). Such approach is efficient in reducing vibrations, but it does not necessarily imply that the noise is reduced most efficiently. However, the virtual microphone control (VMC) approach can be used to appropriately pre-process the error signals obtained by accelerometers to improve noise reduction. Alternatively, other piezoelectric sensors can be applied. The active casing idea can also be extended by appropriately including energy recovery issues or employment of smart materials.^17,18

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: This study was supported by the Ministry for Higher Education and Science,Poland,and by the National Science Centre,Poland (Decision no. DEC-2017/25/B/ST7/02236).

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Liu G, Lu K, Zou D et al. Development of a semi-active dynamic vibration absorber for longitudinal vibration of propulsion shaft system based on magnetorheological elastomer. Smart Mater Struct 2017; 26: 1–16.

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