Underwater Sound Radiation Control by Active Vibration Isolation an Experiment

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DOI: 10.1243/14750902JEME157

223: 5032009oceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment

Z Zhang, X Huang, Y Chen and H HuaUnderwater sound radiation control by active vibration isolation: An experiment

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Underwater sound radiation control by active vibrationisolation: an experimentZ Zhang*, X Huang, Y Chen, and H Hua

State Key Laboratory of Mechanical Systems and Vibration, Shanghai Jiaotong University, Shanghai, Peoples Republic

of China

The manuscript was received on 14 February 2009 and was accepted after revision for publication on 29 June 2009.

DOI: 10.1243/14750902JEME157

Abstract: An experimental system, mainly including a rotary machine, four active vibrationisolators and a water container, was established to investigate the role of active vibration

isolation in suppressing vibration transmission as well as underwater sound radiation. Finiteelement analysis and experimental modal testing were employed to exhibit and validatevibration modes of the fluid-coupled structure and the radiated sound field in water. Soundfield given by this validated finite element model is taken as the substitution for a realmeasurement. In the experiment, the fundamental frequency of the rotary machine was chosento be nearly equal to a natural frequency of the coupled system in order to create a sound fieldin the water container by resonant structural vibration. The rotary machine is supported by thefour electromagnetic vibration isolators, which suppress the quasi-periodical local vibrationindependently according to an adaptive control method. The measured results havedemonstrated that low-frequency sound radiation can be reduced by local active vibrationisolation.

Keywords: active vibration isolation, underwater sound radiation, fluidstructure interaction,

adaptive control

1 INTRODUCTION

Fluidstructure interaction and the pertinent sound

radiation have been thoroughly investigated since

the 1950s, but the research on active control of

sound radiation started very late. Compared with the

abundant work in the active control of structure-

borne sound in the air, there is scant research

concerning active control of vibration and/or sound

radiation from structures in heavy fluid [13].

However, structures filled with and/or surrounded

by heavy fluid are frequently met in applications, for

example, in the area of ship transportation. Vibration

of ship structures induced by power machinery is

harmful to passengers as well as the ocean environ-

ment, especially the vibration at low frequencies,

usually less than several hundred Hertz, is difficult to

control by passive means. Active isolation of vibra-

tions of power machinery is an effective means to

reduce vibration transmission and hence the sound

radiation of structures. There is plenty of research on

active vibration isolation, concerning control algo-

rithms as well as implementation [46]. Vibration of

structures is strongly influenced by heavy fluid at

low frequencies. The added inertia effect of fluid

clearly changes the natural vibration frequencies of

structures and, accordingly, the radiation of sound.

Therefore, fluidstructure interaction should be

considered in the control of low-frequency vibration.

Currently, the commonly used methods in describ-

ing fluidstructure interaction are the finite element

method (FEM) and/or the boundary element

method (BEM). The FEM/BEM methods are superior

in analysing structures coupled with unbounded

domain of fluid [79]. For the analysis of steady-state

structural vibration and sound radiation, the

coupled motion is usually given in the frequency

domain with fluid compressibility taken into ac-count. However, it is more flexible to apply a time

*Corresponding author: State Key Laboratory of Mechanical

Systems and Vibration, Shanghai Jiaotong University, Shanghai,

Peoples Republic of China.email: [email protected]

503

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domain model in simulation and to investigate non-

linearity in active vibration control. In order to carry

out active vibration isolation in real time, a lower

order model that describes the fluidstructure inter-

action with sufficient accuracy is necessary. The

validated numerical model (modal model) and the

directly measured model are appropriate to real-

time control and the latter is preferable in practice

and is adopted in this paper.

Adaptive cancellation is one of the adaptive

strategies that can cancel periodic disturbances

and is used widely in many fields, such as signal

processing as well as control engineering. In active

vibration isolation, cancellation with tracking filters

can suppress tonal vibrations at specified frequen-

cies, but needs online frequency estimation since the

centre frequencies of these filters are adjustedaccording to disturbing forces/moments. Filtered-x

least mean squares (FxLMS) and recursive least

squares are important adaptive control algorithms

and, especially, FxLMS is often used in real applica-

tions owing to its fast computation and easy imple-

mentation. In noise cancellation, FxLMS is used

independently or combined with tracking filters to

control harmonic sound [1012]. FxLMS can also be

applied in the control of low-frequency vibration of

thin plates, where the vibration control involves

fluidstructure interaction [3]. In the control of

engine-induced mount vibration, the multi-channelactive vibration isolation scenario with FxLMS has

achieved notable reduction in vibration [4]. In the

FxLMS algorithm, controller weights are updated

according to error signals and a large disturbance in

the error will lead to excessive adaptation of weights,

which can cause saturation in the controller output

and consequently deteriorate control performance.

For active vibration isolation, saturation will cause

high-frequency vibrations and even resonance in an

isolation system. However, controller saturation in

active vibration isolation has been rarely concerned

[13]. Non-linearity in vibration isolation is compli-cated and is usually related to a particular problem.

In this paper, active vibration isolation and its

influence on the underwater sound field in a

plexiglass water container are discussed by an

experiment, which is the subsequent work of an

early investigation by the authors [9]. The work

demonstrates the effectiveness of active isolation in

the attenuation of sound radiation as well as the

influence of vibration modes to the radiated sound

field. Before conducting the experiment, FEM is first

employed to analyse the coupled vibration andexhibit underwater sound field corresponding to

the natural vibration modes. The numerical model

and results are used to explain the controlled sound

field. In the implementation of active vibration

isolation, the adaptive controller is embedded with

tracking filters. The role of tracking filters is to track

vibration signals of oscillating frequencies. More-

over, saturation in controller output is alleviated by

compressing the updating of weights of the adaptive

controller and accordingly a good performance of

active isolation in the presence of abnormal dis-

turbances can be expected [14].

Detailed discussion is given in five sections. Finite

element analysis and model validation are given in

section 2; section 3 gives a short discussion on the

adaptive control algorithm; Experimental results are

presented in section 4, and conclusions are pre-

sented in section 5.

2 ANALYSIS AND VALIDATION OF THEEXPERIMENTAL MODEL

For the analysis of interaction between structures

and fluid within a finite space, the finite element

method is usually an appropriate choice since the

vibration displacements and sound pressure can be

described by a discrete model of finite degrees of

freedom. The natural vibration modes of the coupled

system are then obtained by solving matrix eigen-

value problems [15]. The purpose of numerical

analysis is to exhibit sound field in the water, which

is usually easy to simulate but difficult to measure.

One part of the experimental model is the

plexiglass water container with a plexiglass plate

installed on its top, as shown in Fig. 1. The wall

thickness of the container is 50 mm and its dimen-

sions are 60067006800 mm (height). The plate is

20 mm thick and the dimensions of the surface in

contact with water are 3006600mm. In the finite

element model, the container is modelled with 8512

solid elements, the plate with 296 shell elements and

the water with 23 013 fluid elements. Mechanical

properties of the materials are listed in Table 1.

The coupling between the container and water is

on the five interfaces where the container contacts

the water. The top surface of the water is partly

coupled with the plate and there are two separate

free water surfaces. In the computation, the pressure

on the free surfaces is set to zero (The effect of air is

neglected and the coupled system is assumed to

vibrate in vacuo). The model without water is first

analysed, and the first four natural frequencies of the

dry plate are listed in Table 2, in which thecomputed results and the measured results obtained

504 Z Zhang, X Huang, Y Chen, and H Hua

Proc. IMechE Vol. 223 Part M: J. Engineering for the Maritime Environment JEME157



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by modal testing are very close. Then, the model

with water is analysed and the first four natural

frequencies of the wet plate are also listed in Table 2.

As can be seen, the computed frequencies are again

close to the measured ones. In Table 2, all the

frequencies of the plate clearly decrease after it is

coupled with the water, which implies a strong

interaction between the plate and the water. Figure 2

gives the first four mode shapes of the plate coupled

with water. In these mode shapes, the first and the

third are bending modes and the second and the

fourth are torsional modes. Pressure distributions

corresponding to the four natural modes are shown

in Fig. 3. As can be seen, the distribution is closely

related to a vibration mode and the maximum

pressure corresponds almost to the largest ampli-

tude of the mode shape.The finite element model was validated by modal

testing. Apart from the natural frequencies, mode

shapes of the plate in the coupled system were also

measured. Figure 4 gives the measurement points as

well as the measured mode shapes. The location of

these points is determined on the basis of computed

mode shapes in order fully to exhibit the node lines

as well as the peak lines. Compared with the shapes

in Fig. 2, the measured shapes have almost the same

peak and node lines.

As the model is validated, one can obtain a

reasonable pressure field in the water container byanalysis. Figures 5(a) and 6(a) are slices of pressure

distribution corresponding respectively to the first

and second natural vibration modes of the plate. The

two slices are at the same location, 150 mm away

from the inside wall surface of the container. In the

slice, 12 observation points are selected, among

which the first three points are near the free surface

and the rest are located 100500 mm below the free

surface with even distance of 50 mm. By dividing the

pressure at every point by the maximum pressure,

one can give normalized values to each point.

Figures 5(b) and 6(b) show the variation of thenormalized values of the 12 points with respect to

the depth. It can be seen from the two figures that

sound fields to the first two vibration modes are

distinct. The sound pressure induced by the first

mode is distributed globally while that by the second

mode is distributed locally. This difference is

attributed to the different radiation directivity of

vibration modes. For the first mode, every point on

the plate vibrates in phase, but for the second mode,

any two points located symmetrically about the

node line vibrates out of phase, resulting in strongdirectivity in the field.

Fig. 1 The water container, plate and water: (a) topview; (b) without water (unmeshed); (c) with

water (meshed)

Underwater sound radiation control by active vibration isolation 505




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The overall experimental system is shown in

Fig. 7. As can be seen, the container is almost full

of water, which contacts the lower surface of the

plexiglass plate. Four active isolators are installed

between the plexiglass plate and an aluminium plate

with dimensions 3006

1806

8 mm. The fan, havingan eccentric mass, is used as a rotary machine and

supported on the aluminium plate. Its nominal

speed is 2400r/min and the nominal fundamental

frequency is therefore 40Hz. The first natural

frequency of the aluminium plate is about 466 Hz,

much higher than this fundamental frequency as

well as the first natural frequency of the plexiglassplate. The active isolators are electromagnetic

Table 1 Mechanical properties

Youngs modulus/bulkmodulus (N/m2) Density (kg/m3) Poissons ratio Sound speed (m/s)

Plexiglass 3.956109 1200 0.35 Water 2.256109 1000 1500

Table 2 Computed and measured natural frequencies of the plate

No water in the container, active isolators not installed

Computed (Hz) 70.3 134.8 213.5 318.3Measured (Hz) 71.40.5 137.50.5 209.20.5 314.0 0.5

Container filled with water, active isolators not installed

Computed (Hz) 28.3 79.0 85.6 190.6Measured (Hz) 29.00.5 78.40.5 89.20.5 186.2 0.5

Container filled with water, active isolators installed

Measured (Hz) 39.40.5 81.30.5 97.00.5 209.5 0.5

Fig. 2 The first four mode shapes of the plate





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actuators. Diameter and height of each actuator are

50 and 40 mm respectively and the first natural

frequency is 66Hz. Natural frequencies of the

plexiglass plate are altered after the installation of

active isolators, which are also measured and listed

in Table 2. The table shows that each natural

frequency becomes larger the first rises to

39.4 Hz, but the second has only a small variation.

Since the first natural frequency is very close to the

fundamental frequency of the fan, the radiated

sound exhibits a strong resonance at this frequency,

as can be observed in the experiment. Theoretically,

not only the natural frequencies but also mode

shapes of the plate will change with the installation

of active isolators, so will the induced sound field.

However, the sound field to the first natural

frequency is similar to that in Fig. 5 because the

plexiglass plate in Fig. 7 can be regarded as a

stiffened one by the actuators and the aluminium

plate.

In the experiment, four accelerometers are in-

stalled beside the active isolators to measure the

responses of the plexiglass plate and one acceler-

ometer on the aluminium plate to measure the

vibration of the fan. Moreover, one sound pressure

transducer is immersed in water to measure the

underwater sound pressure induced by the resonant

vibration of the plexiglass plate. The controller is a

PC with one NI-PCI6259 board inside, which has 32

input channels and 4 output channels.

3 ADAPTIVE METHOD IN ACTIVE VIBRATIONISOLATION

The vibration induced by the rotating eccentric mass

is composed of harmonics. For periodical responses,

the control method adaptive cancellation is an

effective way to counteract the influence of distur-

bance. The adopted adaptive control system is

shown in Fig. 8, where Hs(z) and Hc(z) are the

transfer functions respectively from Fd and Fc to the

vibration acceleration at point S. Fd and Fc represent

respectively the disturbance force and the control

force. In Fig. 8(b), the control force Fc is applied to

cancel the vibration of S induced by the disturbance

force Fd. The reduction of vibration at point S will

result in a decrease of sound radiation from the plate

structure. Adaptation of Fc is realized according to

the vibration of point S, i.e. the error signal. The

adaptive controller is constructed on the FxLMS

algorithm. In the figure, F(z) represents tracking

filters, Hc(z) is the estimate of Hc(z), W(z) the

controller, d(k) the disturbance, e(k) the error signal,

r(k) the reference signal, y(k) the response induced

by u(k).

The discrete transfer function ofF(z)

shown inFig. 8(a) can be described by

Fig. 3 Pressure distribution on the top surface of thewater





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Fig. 4 The first four mode shapes of the plate (left measurement points; right mode shapes)

Fig. 5 Sound field to the first vibration mode: (a) a slice of the sound field (normalized pressure);(b) normalized pressure versus depth





8/14

F z ~ F1 z , F2 z , , Fn z T,

Fi z ~bi0zbi2z

{2

1zai1z{1zai2z{2, i~1*n 1

where ai1~{2exp {fvi=fs cosffiffiffiffiffiffiffiffiffiffiffiffi

1{f2p

vi=fs

, ai2~

exp {2fvi=fs , bi0~1=2 1{ exp {2fvi=fs , bi25

2bi0, fs is the sampling frequency. In the adaptive

isolation, the centre frequencies vi of F(z) are

estimated by online frequency estimators.

For each adaptive controller Wi(z), the adaptation

of its coefficients can be given by equation (2)according to the LMS algorithm

wi kz1 ~wi k zmei k

cz ri k k k2ri k

u k ~P

i

wTi k ri k , i~1*n 2

where ri(k) is the output of Hc(z) under the inputri(k), r(k)5 (r1(k),r2(k),...,rn(k))

T, ei(k) the output ofFi(z) under the input e(k), m is an adjustingparameter, c. 0. However, in this paper, equation(2) is replaced by a modified formula.

Since the control signal u(k) is the output of W(z)

under the input r(k), and one step update of coeffi-cients of W(z) given in equation (2) is proportional

Fig. 6 Sound field to the second vibration mode: (a) a slice of the sound field (normalizedpressure); (b) normalized pressure versus depth





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to the filtered error signal ei(k), excessive adaptation

will occur when there is a large shock in the error

signal, which can result in saturation in controlleroutput. Output saturation can produce high-fre-

quency excitation and even instability, which will

deteriorate vibration isolation. Therefore, the adap-

tation formula in equation (2) should be modified to

consider this circumstance. For an ideal saturation

sat u k ~

d, u k wd

u k , u k j jd

{d, u k v{d

8>: , dw0 3

the following formula can be deduced by solving anoptimization problem [14]

Fig. 7 Experimental system for active vibration isola-

tion and underwater sound radiation control:(a) photograph; (b) front view; (c) top view

Fig. 8 Active isolation and the adaptive controlscheme with tracking filters





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wi kz1

~fu wTi k ri k

wi k zmei k

cz ri k k k2ri k

!

4

where fu wTi k ri k

is the derivative of a sigmoid

function f(u) with respect to the variable u. Accord-

ing to the definition of sigmoid functions, as u(k)

approaches saturation, fu wTi k ri k

decreases fast

to zero and consequently reduce the adaptation

step of wi(k). This property guarantees that

fu wTi k ri k

is able to weaken any excessive

updating of wi(k) and alleviate output saturation.

Moreover, equation (4) can degrade to equation (2)

as long as no output saturation occurs.

4 EXPERIMENTAL RESULTS

Figure 9 is the measured fundamental frequency of

the fan, which indicates that the rotation speed is

not constant but oscillates between 40.5 and 41.1 Hz.

In the figure, there are 4800 samples in total,

corresponding to a 12 s record under the sampling

frequency 400 Hz. Therefore, the oscillation fre-

quency of the speed is very small as compared with

the fundamental frequency. The given adaptive

algorithm with real-time tracking filters is not

sensitive to the variation of speed, which can

guarantee a large attenuation of quasi-periodical

vibrations even under unsteady excitation.

Transfer functions from the control voltage to the

local acceleration responses at the four active

isolators are measured for further implementation

of active isolation. Figure 10 gives the measured

frequency response functions (FRFs), and the FRF

from the control voltage of the second active isolator

to the measured sound pressure at point 4 (marked

in Figs 5 and 6) is also shown for comparison. The

following conclusions can be drawn from these

measured curves.

1. FRFs of the four active isolators are almost the

same except at the natural frequencies.2. In the pressure/voltage curve, all peaks corre-

spond to the natural frequencies of the plate as

well as the active isolators, and at the observation

point, sound pressure induced by the second

mode (at 81 Hz) is stronger than the other three

modes of the plate.

3. When excited by white noise, natural vibration of

the active isolators will create higher sound

pressure than the first four modes of the plate,

which implies that the natural vibration should be

damped in the implementation of active isolation.

With the measured FRFs of active isolators and the

adaptive control structure shown in Fig. 8, active

control is implemented and each active isolator

generates cancelling forces according to the local

vibration accelerations to counteract vibration

caused by the rotating fan and the corresponding

radiated sound. Since the excitation of the fan is

mainly composed of vibration at the fundamental

frequency and forces the plate to vibrate resonantly

at its first natural frequency, the spectrum of

radiated sound from the plate at the fundamental

frequency is dominant when no control is imple-mented. After active control, the radiation at the

fundamental frequency is suppressed substantially,

as shown in Fig. 11, where the spectrum at the first

natural frequency of the isolator (about 66 Hz) is

raised to some extent. In the resonant condition, the

pressure at those points shown in Fig. 5 was

measured and the results are given in Table 3, from

which one can see that the trend implied by the

pressure-depth data is similar to that shown in

Fig. 5.

Figure 12 gives the acceleration responses at the

foot of the second active isolator before and after

Fig. 9 The fundamental frequency of the fan





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active isolation respectively, from which it can be

seen that vibration at the fundamental frequency

(around 40.8 Hz) is suppressed by 90 per cent, but

increases at the second and the fifth harmonic

frequencies (near 81, 205 Hz), and clearly rises at

the first natural frequency of the isolator (about66 Hz). Comparing Fig. 12 with Fig. 11, it can be seen

that the spectra of sound pressure at the second and

fifth harmonic frequencies keep almost the same

except at around 66 Hz, which increases by almost

20 dB. Nevertheless, the total vibration and sound

are attenuated by a large percentage. The reason for

this phenomenon is that the radiated sound field atabout 81 or 205 Hz has strong directivity and the

Fig. 10 Measured FRFs of the control channels: (a) acceleration versus voltage; (b) pressureversus voltage





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measurement point is not in the radiation direction,

which renders the measured sound pressure insen-

sitive to the variation of vibration of the plate. The

directivity is closely related to forced vibration

modes of the plate, and the two vibration modes at

81 and 205 Hz are actually similar to those given in

Fig. 5.

5 CONCLUSION

Active vibration isolation and sound radiation of an

experimental system with fluidstructure interaction

are discussed. The vibration characteristics of the

plate coupled with water in a plexiglass container areanalysed by the FEM and validated by modal testing,

which forms a base for the explanation of controlled

sound radiation in the water container. Active

vibration isolation is realized on the basis of an

adaptive algorithm with embedded tracking filters

that are used to ensure the control process insensi-

tive to the fluctuation of vibration frequencies. Four

actuators operate independently to cancel local

vibrations at each active isolator. The vibration and

radiated sound at the fundamental frequency are

suppressed substantially after active isolation. At

certain high-order harmonic frequencies, vibration

of the plate increases but results in indiscernible

change in sound pressure. The radiated sound field

is closely related to vibration modes, those modes ofstrong directivity in radiation induce only local

Fig. 11 Sound pressure before and after control (Ref5161026 Pa and depth 5 500 mm):(a) time domain responses: (b) spectra

Table 3 Sound pressure at different locations (Hanning window and linear average)

No. 1 2 3 4 5 6 7 8 9 A B C

Depth (mm) 5 10 25 100 150 200 250 300 350 400 450 500Sound pressure (Pa) 3.4 10.2 29.8 97.9 103.3 102.1 102.9 103.9 101.6 101.2 99.6 99.0





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radiation, having weak influence on the sound

pressure at locations away from the radiation

direction, which usually cause a discrepancy in the

attenuation of vibration and sound at certain

harmonic frequencies after active isolation.

ACKNOWLEDGEMENT

This work was fully supported by the NSF of China(Grant No. 10672099).

F Authors 2009

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APPENDIX

Notation

ai1, ai2, bi0,

bi0, bi2

coefficients of the ith tracking

filterd(k) disturbance

e(k) error signal

fs sampling frequency

f(u) sigmoid function

Fd, Fc disturbance force, control force

F(z)5 (F1(z),

F2(z),...,Fn(z))T

tracking filters

Hc(z), Hs(z) transfer functions

Hc(z) estimate of Hc(z)

r(k)5 (r1(k),

r2(k),...,rn(k))T

reference signals

u(k) control signal

wi(k) weight vector of the ith controller

W(z)5 (w1(z),

w2(z),...,wn(z))T

controller

y(k) response signal induced by u(k)

ei(k) output of Fi(z)

m, c. 0, d. 0 scalar variables

ri(k) output of Hc(z)

vi centre frequency



Documents

Underwater Sound Radiation Control by Active Vibration Isolation an Experiment